BÀI 1: QUÁ TRÌNH NGUỘI CỐC CAFE (BẬC 1)
function baitoan1
clear all;clc;close all;
T=dsolve('DT=-r*(T-Tp)','T(0)=T0','t');
fprintf('bieu thuc cua T theo t la: ');pretty(T);
syms Tp T0 r t
% T=Tp+(T0-Tp)*exp(-r*t);
ti=0:2:46;
Tcd=[82.3,78.5,74.3,70.7,67.6,65.0,62.5,60.1,58.1,56.1,54.3,52.8,51
.2,49.9,48.6,47.2,46.1,45.0,43.9,43.0,41.9,41.0,40.1,39.5];
Tcs=[68.8,64.8,62.1,59.9,57.7,55.9,53.9,52.3,50.8,49.5,48.1,46.8,45
.9,44.8,43.7,42.6,41.7,40.8,39.9,39.3,38.6,37.7,37.0,36.4];
plot(ti,Tcd,'*-r');hold on; grid on;
ylabel('nhiet do (do C)');xlabel('thoi gian(phut)');
title('qua trinh nguoi cua coc cafe den');
Td=subs(T,[Tp,T0],[17,82.3]);
funTd=inline(vectorize(Td),'r','t');
r0d=0.025;
rnd=lsqcurvefit(funTd,r0d,ti,Tcd);
fprintf('hang so nguoi la'),rnd
yyd=funTd(rnd,ti);
plot(ti,yyd,'+-b');
legend('duong thuc nghiem','duong ly thuyet');
%tim thoi gian khi coc cafe co nhiet do 50 va 30
Td=subs(Td,r,rnd);
fprintf('bieu thuc nhiet do T cua coc cafe theo thoi gian t
la:');pretty(Td);
figure(2);
ezplot(Td,[0 80]);grid on;
t50d=double(solve(Td-50));
fprintf('thoi gian de coc cafe co nhiet do 50do la: '),t50d

t30d=double(solve(Td-30));
fprintf('thoi gian de coc cafe co nhiet do 30do la: '),t30d
figure(3);
plot(ti,Tcs,'*-r');hold on;grid on;
ylabel('nhiet do (do C)');xlabel('thoi gian(phut)');
title('qua trinh nguoi cua coc cafe sua');
Ts=subs(T,[Tp,T0],[17,68.8]);
funTs=inline(vectorize(Ts),'r','t');
r0s=0.023;
rns=lsqcurvefit(funTs,r0s,ti,Tcs);
fprintf('hang so nguoi la'),rns
1


yys=funTs(rns,ti);
plot(ti,yys,'+-b');
legend('duong thuc nghiem','duong ly thuyet');
%tim thoi gian khi coc cafe co nhiet do 50 va 30
Ts=subs(Ts,r,rns);
fprintf('bieu thuc nhiet do T cua coc cafe theo thoi gian t
la:');pretty(Ts);
figure(4);
ezplot(Ts,[0 80]);grid on;
t50s=double(solve(Ts-50));
fprintf('thoi gian de coc cafe co nhiet do 50do la: '),t50s
t30s=double(solve(Ts-30));
fprintf('thoi gian de coc cafe co nhiet do 30do la: '),t30s
%
%
%

%
%
%
%
%
%
%
%
%
%
%
%
%

bieu thuc cua T theo t la:
Tp + exp(-r t) (-Tp + T0)
hang so nguoi la: rnd =0.0259
bieu thuc nhiet do T cua coc cafe theo thoi gian t la:
653
7471411333879989
17 + --- exp(- ------------------ t)
10
288230376151711744
thoi gian de coc cafe co nhiet do 50do la:t50d =26.3287
thoi gian de coc cafe co nhiet do 30do la:t30d = 62.2662
hang so nguoi la: rns = 0.0237
bieu thuc nhiet do T cua coc cafe theo thoi gian t la:
3415481214600901
17 + 259/5 exp(- ------------------ t)
144115188075855872

thoi gian de coc cafe co nhiet do 50do la: t50s =19.0249
thoi gian de coc cafe co nhiet do 30do la: t30s =58.3317

####DẠNG KHÁC
function baitoan1_2
clear all;clc;close all;
T=dsolve('DT=-r*(T-Tp)','T(0)=T0','t');
disp('bieu thuc nhiet do: T(t)=');pretty(T);
syms r T0 Tp t
ti=0:2:46;
while (1)
k=menu('hang so nguoi','cafe den','cafe sua','thoat');
switch k
case 1
Tcd=[82.3,78.5,74.3,70.7,67.6,65.0,62.5,60.1,58.1,56.1,54.3,52.8,51
.2,49.9,48.6,47.2,46.1,45.0,43.9,43.0,41.9,41.0,40.1,39.5];
2


figure(1);
plot(ti,Tcd,'r');hold on;grid on;
nr=input('cho gan dung ban dau r la: '); %0.025
Tcdt=subs(T,[r,T0,Tp],[nr,Tcd(1),17]);
Tcdt=subs(Tcdt,t,ti);
plot(ti,Tcdt,'b');
ylabel('nhiet do (do C)');xlabel('thoi gian(phut)');
title('qua trinh nguoi cua coc cafe den');
legend('duong thuc nghiem',['duong ly thuyet voi r =',
num2str(nr)]);hold off;
case 2

Tcs=[68.8,64.8,62.1,59.9,57.7,55.9,53.9,52.3,50.8,49.5,48.1,46.8,45
.9,44.8,43.7,42.6,41.7,40.8,39.9,39.3,38.6,37.7,37.0,36.4];
figure(2);
plot(ti,Tcs,'r');hold on;grid on;
nr=input('cho gan dung ban dau r la: '); %0.023
Tcst=subs(T,[r,T0,Tp],[nr,Tcs(1),17]);
Tcst=subs(Tcst,t,ti);
plot(ti,Tcst,'b');
ylabel('nhiet do (do C)');xlabel('thoi gian(phut)');
title('qua trinh nguoi cua coc cafe den');
legend('duong thuc nghiem',['duong ly thuyet voi r =',
num2str(nr)]);hold off;
case 3
break
end
end

BÀI 2: QUÁ TRÌNH NGUỘI CỐC CAFE (BẬC 2)
function baitoan2
clear all;clc;close all;
T=dsolve('DT=-r2*(T-Tp)^2-r1*(T-Tp)','T(0)=T0','t');
fprintf('bieu thuc cua T theo t la: ');pretty(T);
syms Tp T0 r1 r2 t
ti=0:2:46;
Tcd=[82.3,78.5,74.3,70.7,67.6,65.0,62.5,60.1,58.1,56.1,54.3,52.8,51
.2,49.9,48.6,47.2,46.1,45.0,43.9,43.0,41.9,41.0,40.1,39.5];
plot(ti,Tcd,'*-r');hold on; grid on;
ylabel('nhiet do (do C)');xlabel('thoi gian(phut)');
title('qua trinh nguoi cua coc cafe den');
Td=subs(T,{Tp,T0,r1,r2},{17,'a(1)','a(2)','a(3)'});

3


funTd=inline(vectorize(Td),'a','t');
r0d=[82.3 0.006 0.0004];
rnd=lsqcurvefit(funTd,r0d,ti,Tcd);
%fprintf('hang so nguoi la:'),r1=rnd(2),r2=rnd(3)
fprintf(['hang so nguoi r1= ',num2str(rnd(2)),' va r2=
',num2str(rnd(3)),'\n']);
yyd=funTd(rnd,ti);
plot(ti,yyd,'+-b');
legend('duong thuc nghiem','duong ly thuyet');
%tim thoi gian khi coc cafe co nhiet do 50 va 30
Td=subs(Td,{'a(1)','a(2)','a(3)'},{rnd(1),rnd(2),rnd(3)});
%fprintf('bieu thuc nhiet do T cua coc cafe theo thoi gian t
la:');pretty(Td);
fprintf(['bieu thu nhiet do T cua coc cafe theo thoi gian t la:
\n',char(vpa(Td,3)),'\n']);
figure(2);
ezplot(Td,[0 120]);grid on;
t50d=double(solve(Td-50));
fprintf('thoi gian de coc cafe co nhiet do 50do la: '),t50d
t30d=double(solve(Td-30));
fprintf('thoi gian de coc cafe co nhiet do 30do la: '),t30d
% bieu thuc cua T theo t la:
%
r1 - r2 Tp + T0 r2
%
r1 + Tp exp(t r1 + log(- ------------------)) - r2
Tp

%
Tp - T0
%
- ---------------------------------------------------%
r1 - r2 Tp + T0 r2
%
-exp(t r1 + log(- ------------------)) + r2
%
Tp - T0
% hang so nguoi r1= 0.0071874 va r2= 0.00042365
% bieu thu nhiet do T cua coc cafe theo thoi gian t la:
% (.147e-4-17.*exp(.719e-2*t-7.54))/(-1.*exp(.719e-2*t-7.54)+.424e3)
% thoi gian de coc cafe co nhiet do 50do la: t50d =25.6294
% thoi gian de coc cafe co nhiet do 30do la: t30d =84.1027

4


BÀI 3: PHÂN HỦY HẠT NHÂN

Kr

Br

Se

function baitoan3
clear all;clc;close all;
T1=14.8;T2=16.1;
% lamda1=log(2)/T1;lamda2=log(2)/T2;

% d1='DN1=-ld1*N1';
% d2='DN2=-ld2*N2+ld1*N1';
% d3='DN3=ld2*N2';
% d=[d1,',',d2,',',d3];
% dkbd='N1(0)=1,N2(0)=0,N3(0)=0';
% dsol=dsolve(d,dkbd,'t');
% syms ld1 ld2 t
% N1t=subs(dsol.N1,ld1,lamda1);
% N2t=subs(dsol.N2,[ld1,ld2],[lamda1,lamda2]);
% N3t=subs(dsol.N3,[ld1,ld2],[lamda1,lamda2]);
ld1=log(2)/T1;ld2=log(2)/T2;
d1='DN1=-ld1*N1';
d2='DN2=-ld2*N2+ld1*N1';
d3='DN3=ld2*N2';
d=[d1,',',d2,',',d3];
dkbd='N1(0)=1,N2(0)=0,N3(0)=0';
dsol=dsolve(d,dkbd,'t');
N1t=subs(dsol.N1);
N2t=subs(dsol.N2);
N3t=subs(dsol.N3);
% ti=0:2:200;
% N1ti=subs(N1t,t,ti);
% plot(ti,N1ti,'r');
ezplot(N1t,[0 200]);hold on;grid on;
h1=ezplot(N2t,[0 200]);set(h1,'color',[1 0 0]);
h2=ezplot(N3t,[0 200]);set(h2,'color',[0 1 0]);
title('qua trinh phan huy Kr');
legend('Kr','Br','Se');
ylabel('khoi luong (mg)');
xlabel('thoi gian (gio)');

%khi mBr max
[x0,y0]=ginput(1);
% n2ti=inline(['-1*(',vectorize(N2t),')'],'t');
n2ti=inline(vectorize(-N2t),'t');
[xn,yn]=fminsearch(n2ti,x0,optimset('display','off'));
fprintf(['Br co khoi luong lon nhat la m= ',num2str(-yn),' tai t=
',num2str(xn),'\n']);
%khi mBr=mKr
[x01,y01]=ginput(1);
5


n12ti=inline(vectorize(-N2t+N1t),'t');
[xn1,yn1]=fsolve(n12ti,x01,optimset('display','off'));
fprintf(['Br co khoi luong bang Kr tai t= ',num2str(xn1),' khi do
mBr= ',num2str(-n2ti(xn1)),'\n']);
%khi mBr=mSe
[x02,y02]=ginput(1);
n23ti=inline(vectorize(-N2t+N3t),'t');
[xn2,yn2]=fsolve(n23ti,x02,optimset('display','off'));
fprintf(['Br co khoi luong bang Se tai t= ',num2str(xn2),' khi do
mBr= ',num2str(-n2ti(xn2)),'\n']);
% Br co khoi luong lon nhat la m= 0.38347 tai t= 22.2634
% Br co khoi luong bang Kr tai t= 20.5336 khi do mBr= 0.38225
% Br co khoi luong bang Se tai t= 28.763 khi do mBr= 0.37

BÀI 4: PHÂN HỦY HẠT NHÂN THEO 2 NHÁNH
Rn
Rn


26%Po
74%At

Bi
Po

Pb
Pb

function baitoan4
clear all; clc; close all;
TRn=15; TPo207=5.7; TBi=30*365*24; TAt=7.2; TPo211=0.52/3600;
lRn=log(2)/TRn;lPo207=log(2)/TPo207;lBi=log(2)/TBi;lAt=log(2)/TAt;l
Po211=log(2)/TPo211;
f1='DNRn=-lRn*NRn';
f21='DNPo207=-lPo207*NPo207+26/100*lRn*NRn';
f31='DNBi=-lBi*NBi+lPo207*NPo207';
f22='DNAt=-lAt*NAt+74/100*lRn*NRn';
f32='DNPo211=-lPo211*NPo211+lAt*NAt';
f=[f1,',',f21,',',f31,',',f22,',',f32];
dkbd='NRn(0)=1, NPo207(0)=0, NBi(0)=0, NAt(0)=0, NPo211(0)=0';
dsol=dsolve(f,dkbd,'t');
NRnt=subs(dsol.NRn);
NPo207t=subs(dsol.NPo207);
NBit=subs(dsol.NBi);
NAtt=subs(dsol.NAt);
NPo211t=subs(dsol.NPo211);
NPbt=1-(NRnt+NPo207t+NBit+NAtt+NPo211t);
6



ti=linspace(0,100);
subplot(3,2,1);ezplot(NRnt,[0 100]);grid on;title('Rn');
subplot(3,2,3);ezplot(NPo207t,[0 100]);grid on;title('Po207');
subplot(3,2,5);ezplot(NBit,[0 300]);grid on;title('Bi');
subplot(3,2,2);ezplot(NAtt,[0 100]);grid on;title('At');
subplot(3,2,4);NPo211i=double(subs(NPo211t,'t',sym(ti)));plot(ti,NP
o211i);grid on;title('Po211');
subplot(3,2,6);NPbi=double(subs(NPbt,'t',sym(ti)));plot(ti,NPbi);gr
id on;title('Pb');
%thoi diem cac nguyen to At,Po211,Po207 va Bi co khoi luong cuc dai
NAti=inline(vectorize(-NAtt),'t');
[t0,m0]=ginput(1);
[tn,mn]=fminsearch(NAti,t0,optimset('display','off'));
fprintf(['At co khoi luong lon nhat la m= ',num2str(-mn),' tai t=
',num2str(tn),'\n']);
NPo211i=inline(vectorize(-NPo211t),'t');
[t01,m01]=ginput(1);
[tn1,mn1]=fminsearch(NPo211i,t01,optimset('display','off','tolfun',
1e-12,'tolx',1e-12));
%mn1=double(subs(NPo211i,'t',sym(tn1)));
mn1=NPo211i(tn1);
fprintf(['Po211 co khoi luong lon nhat la m= ',num2str(-mn1),' tai
t= ',num2str(tn1),'\n']);
NPo207i=inline(vectorize(-NPo207t),'t');
[t02,m02]=ginput(1);
[tn2,mn2]=fminsearch(NPo207i,t02,optimset('display','off'));
fprintf(['Po207 co khoi luong lon nhat la m= ',num2str(-mn2),' tai
t= ',num2str(tn2),'\n']);
NBii=inline(vectorize(-NBit),'t');

[t03,m03]=ginput(1);
[tn3,mn3]=fminsearch(NBii,t03,optimset('display','off'));
fprintf(['Bi co khoi luong lon nhat la m= ',num2str(-mn3),' tai t=
',num2str(tn3),'\n']);
%Thoi diem khi mPb=1/3mRn va mPb=2/3mRn
figure(2);
NPb13Rn=inline(vectorize(NPbt-1/3*NRnt),'t');
NPb13Rni=double(subs(NPbt,'t',sym(ti))-1/3*subs(NRnt,'t',sym(ti)));
plot(ti,NPb13Rni,'r');grid on;hold on;
[tn130,mn130]=ginput(1);
7


[tn13,mn13]=fsolve(NPb13Rn,tn130,optimset('display','off','tolfun',
1e-12,'tolx',1e-12));
mn13=double(subs(NPbt,'t',sym(tn13)));
fprintf(['Pb co khoi luong bang 1/3Rn tai t= ',num2str(tn13),' khi
do mPb= ',num2str(mn13),'\n']);
NPb23Rn=inline(vectorize(NPbt-2/3*NRnt),'t');
NPb23Rni=double(subs(NPbt,'t',sym(ti))-2/3*subs(NRnt,'t',sym(ti)));
plot(ti,NPb23Rni,'b');
[tn230,mn230]=ginput(1);
[tn23,mn23]=fsolve(NPb23Rn,tn230,optimset('display','off','tolfun',
1e-12,'tolx',1e-12));
mn23=double(subs(NPbt,'t',sym(tn23)));
fprintf(['Pb co khoi luong bang 2/3Rn tai t= ',num2str(tn23),' khi
do mPb= ',num2str(mn23),'\n']);
%
%
%

%
%
%

At co
Po211
Po207
Bi co
Pb co
Pb co

khoi luong lon nhat la m=
co khoi luong lon nhat la
co khoi luong lon nhat la
khoi luong lon nhat la m=
khoi luong bang 1/3Rn tai
khoi luong bang 2/3Rn tai

0.1804 tai t= 14.6616
m= NaN tai t= 13.2432
m= 0.054602 tai t= 12.8336
0.25985 tai t= 221.8078
t= 13.9401 khi do mPb= 0.17124
t= 19.2396 khi do mPb= 0.26222

BÀI 5: NÉM XIÊN VỚI

Fms = k.v

function baitoan5

clear;close all;clc;
m=0.1;h0=15;v0=30;alpha=pi/6;k=0.15;g=9.8;
f1='D2x=-k/m*Dx';
f2='D2y=-k/m*Dy-g';
f=[f1,',',f2];
int='x(0)=0,Dx(0)=v0*cos(alpha),y(0)=h0,Dy(0)=v0*sin(alpha)';
fs=dsolve(f,int,'t');
x=subs(fs.x,{'m','h0','v0','alpha','k','g'},{m,h0,v0,alpha,k,g});
y=subs(fs.y,{'m','h0','v0','alpha','k','g'},{m,h0,v0,alpha,k,g});
vx=diff(x);vy=diff(y);
subplot(2,2,1);ezplot(x,[0 4]);title('do thi x theo thoi
gian');grid on;
subplot(2,2,2);ezplot(y,[0 4]);title('do thi y theo thoi
gian');grid on;
subplot(2,2,3);ezplot(vx,[0 4]);title('do thi vx theo thoi
gian');grid on;
8


subplot(2,2,4);ezplot(vy,[0 4]);title('do thi vy theo thoi
gian');grid on;
figure(2);
ezplot(x,y);title('do thi quy dao');grid on;
axis([0 20 0 25]);
%khi co ma sat vat di xa duoc xn
tn=double(solve([char(y),'=0'],'t'));tn=tn(1,1);
xn=subs(x,'t',tn);
%khi khong co ma sat vat di xa duoc mot khoang la xn1
%thay doi lai cac dieu kien ban dau khi ko co ma sat
f11='D2x=0';

f21='D2y=-g';
ff=[f11,',',f21];
fs1=dsolve(ff,int,'t');
tn1=double(solve([char(subs(fs1.y,{'m','h0','v0','alpha','k','g'},{
m,h0,v0,alpha,k,g})),'=0'],'t'));
tn1=tn1(2,1);
xn1=subs(subs(fs1.x,{'m','h0','v0','alpha','k','g'},{m,h0,v0,alpha,
k,g}),'t',tn1);
fprintf(['khi khong co ma sat vat se di xa them duoc mot khoang nua
la: ',num2str(xn1-xn),'m\n']);
%thoi diem va do cao vat dat do cao cuc dai
figure(1);
[t0,y0]=ginput(1);
yinl=inline(vectorize(-y),'t');
[tmax,ymax]=fminsearch(yinl,t0,optimset('display','off'));
fprintf(['do cao cuc dai cua vat la: h=',num2str(-ymax),'m',' tai
thoi diem: t= ',num2str(tmax),'s\n']);
%xac dinh goc nem toi uu de vat co the di xa nhat
fx=subs(fs.x,{'h0','m','v0','k','g'},{h0,m,v0,k,g});
fy=subs(fs.y,{'h0','m','v0','k','g'},{h0,m,v0,k,g});
phi=linspace(-pi/2,pi/2,20);
for i=1:length(phi)
fy1=subs(fy,'alpha',phi(i));
fx1=subs(fx,'alpha',phi(i));
t1=double(solve([char(fy1),'=0'],'t'));
for j=1:length(t1)
if t1(j)>0
tmax=t1(j);
end
end

9


xmax(i)=subs(fx1,'t',tmax);
end
sp=spline(phi,xmax);
figure(3);
fnplt(sp,[-pi/2 pi/2]);grid on;
figure(3);
[phi0,xmax0]=ginput(1);
[phin,xmaxn]=fminsearch(@(phi)ppval(sp,phi),phi0,optimset('display','off'));
fprintf(['goc nem toi uu la: phi= ',num2str(phin*180/pi),'do',' va
khi do xmax= ',num2str(-xmaxn),'m\n']);
% khi khong co ma sat vat se di xa them duoc mot khoang nua la:
82.8627m
% do cao cuc dai cua vat la: h=19.8052m tai thoi diem: t= 0.79515s
% goc nem toi uu la: phi= 2.5671do va khi do xmax= 19.7866m

BÀI 6: NÉM XIÊN VỚI Fms = k.v2
function baitoan6
clear all;close all;clc;
m=0.1; h0=15; v0=30; alpha=pi/6; g=9.8; vth=6; k=m*g/vth^2;
% u1=x;
% u2=y;
% u1'=u3=vx
% u2'=u4=vy
% u3'=-k/m*sqrt(u3^2+u4^2)*u3;
% u4'=-k/m*sqrt(u3^2+u4^2)*u4;
f=inline(['[u(3);u(4);',num2str(k/m),'*sqrt(u(3)^2+u(4)^2)*u(3);',...
num2str(-k/m),'*sqrt(u(3)^2+u(4)^2)*u(4)',num2str(g),']'],'t','u');

%odeset('abstol',1e-12,'reltol',1e-12);
[t,u]=ode45(f,[0 4],[0 h0 v0*cos(alpha) v0*sin(alpha)]);
%tim thoi diem vat tiep dat
sp=spline(t,u(:,2));
fnplt(sp,[0 4],'r');grid on;
[ty0 y0]=ginput(1);
[tn yn]=fsolve(@(t)ppval(sp,t),ty0,optimset('display','off'));
[t,u]=ode45(f,[0 tn],[0 h0 v0*cos(alpha) v0*sin(alpha)]);
plot(u(:,1),u(:,2),'r');grid on;title('do thi quy
dao');xlabel('x');ylabel('y');

10


figure(2);
subplot(2,2,1);plot(t,u(:,1));title('do thi x theo thoi gian');grid
on;xlabel('t');ylabel('x');
subplot(2,2,2);plot(t,u(:,2));title('do thi y theo thoi gian');grid
on;xlabel('t');ylabel('y');
subplot(2,2,3);plot(t,u(:,3));title('do thi vx theo thoi
gian');grid on;xlabel('t');ylabel('vx');
subplot(2,2,4);plot(t,u(:,4));title('do thi vy theo thoi
gian');grid on;xlabel('t');ylabel('vy');
%tinh khoang cach vat co the di xa them khi khong co ma sat
%khi khong co mat sat he ptvp se tra thanh
% u1=x;
% u2=y;
% u1'=u3=vx
% u2'=u4=vy
% u3'=0;

% u4'=-g;
f1=inline(['[u(3);u(4);0;-',num2str(g),']'],'t','u');
[t1,u1]=ode45(f1,[0 10],[0 h0 v0*cos(alpha) v0*sin(alpha)]);
sp1=spline(t1,u1(:,2));sp2=spline(t1,u1(:,1));
figure(3);
fnplt(sp1,[0 4],'r');grid on;
[ty01 y01]=ginput(1);
[tn1 yn1]=fsolve(@(t)ppval(sp1,t1),ty01,optimset('display','off'));
fprintf(['khi khong co ma sat vat se di xa them duoc mot khong nua
la: ',num2str(ppval(sp2,tn1)-u(end,1)),'m\n']);
%xac dinh thoi diem va vi tri vat o do cao cuc dai
figure(2);
[ty02 y02]=ginput(1);
[tn2 yn2]=fminsearch(@(t)ppval(sp,t),ty02,optimset('display','off'));
fprintf(['do cao cuc dai cua vat la:
h=',num2str(ppval(sp,tn2)),'m',' tai thoi diem: t=
',num2str(tn2),'s\n']);
%xac dinh goc nem toi uu de vat co the di xa nhat
phi=linspace(-pi/2,pi/2,20);
for i=1:length(phi)
[t2,u2]=ode45(f,[0 5],[0 h0 v0*cos(phi(i)) v0*sin(phi(i))]);
xmax(i)=u2(end,1);
end
sp3=spline(phi,xmax);
figure(3);fnplt(sp3,[phi(1) phi(end)],'r');grid on;
[phi0,xmax0]=ginput(1);
11


[phi,xmax]=fminsearch(@(phi)ppval(sp3,phi),phi0,optimset('display','off'));

fprintf(['goc nem toi uu la: phi= ',num2str(phi*180/pi),'do',' va
khi do xmax= ',num2str(-xmax),'m\n']);
% khi khong co ma sat vat se di xa them duoc mot khong nua la:
90.7651m
% do cao cuc dai cua vat la: h=17.2306m tai thoi diem: t= 0.51164s
% goc nem toi uu la: phi= 10.0363do va khi do xmax= 9.7807m

BÀI 7: NÉM BÓNG CHẠM TƯỜNG
function baitoan7
close all;clear;clc;
m=0.1;h0=10;v0=20;alpha=pi/6;l=15;k=0.1;g=9.8;
eqs=inline(['[y(3);y(4);-',num2str(k/m),'*y(3);-',num2str(k/m),...
'*y(4)-',num2str(g),']'],'t','y');
odeset('abstol',1e-12,'reltol',1e-12);
[t,y]=ode45(eqs,[0,3],[0 h0 v0*cos(alpha) v0*sin(alpha)]);
% Cau a:
spx=spline(t,y(:,1));
spy=spline(t,y(:,2));
figure(1);fnplt(spx,[0,3],'r');grid on;
[t0,x0]=ginput(1);
[t1,x1]=fsolve(@(t)(ppval(spx,t)-l),t0,optimset('display','off'));
h1=ppval(spy,t1);
fprintf(['Thoi diem qua bong cham tuong la: ',num2str(t1),...
's luc nay no co do cao: ',num2str(h1),'m \n']);
% Cau b:
figure(2);plot(t,y(:,2),'r');grid on;title('y(t)');
[t0,y0]=ginput(1);
[t2,x2]=fsolve(@(t)ppval(spy,t),t0,optimset('display','off'));
fprintf(['Thoi diem qua bong cham dat la: ',num2str(t2),...
's luc nay no cach tuong: ',num2str(ppval(spx,t2)-l),'m \n']);

[ti1,y1]=ode45(eqs,[0,t1],[0 h0 v0*cos(alpha) v0*sin(alpha)]);
[ti2,y2]=ode45(eqs,[t1,t2],[l h1 -y1(end,3) y1(end,4)]);
figure(3);
subplot(2,2,1);plot([ti1;ti2],[y1(:,1);y2(:,1)],'r');grid
on;title('x(t)');
subplot(2,2,2);plot([ti1;ti2],[y1(:,2);y2(:,2)],'r');grid
on;title('y(t)');
12


subplot(2,2,3);plot([ti1;ti2],[y1(:,3);y2(:,3)],'r');grid
on;title('vx(t)');
subplot(2,2,4);plot([ti1;ti2],[y1(:,4);y2(:,4)],'r');grid
on;title('vy(t)');
% Cau c:
Al=linspace(-pi/2,pi/2,10);
for i=1:length(Al)
[t,y]=ode45(eqs,[0,5],[0 h0 v0*cos(Al(i)) v0*sin(Al(i))]);
spx=spline(t,y(:,1));spy=spline(t,y(:,2));
%figure(4);fnplt(spy,[0,5],'r');grid on;
%[t0,y0]=ginput(1);
t0=4.5;
[tn,yn]=fsolve(@(t)ppval(spy,t),t0,optimset('display','off'));
xmax(i)=ppval(spx,tn);
end;
sp=spline(Al,xmax);figure(4);fnplt(sp,[-pi/2 pi/2],'r');grid on;
[Al0,xmax0]=ginput(1);
[Al,xmax]=fminsearch(@(Al)-ppval(sp,Al),Al0);xmax=-xmax-l;
fprintf(['Goc nem toi uu khi co ma sat la: ',num2str(Al*180/pi),...
'do, luc nay no cach tuong: ',num2str(xmax),'m \n']);

% Khi khong co ma sat:
eqs=inline(['[y(3);y(4);0;-',num2str(g),']'],'t','y');
Al=linspace(-pi/2,pi/2,10);
for i=1:length(Al)
[t,y]=ode45(eqs,[0,5],[0 h0 v0*cos(Al(i)) v0*sin(Al(i))]);
spx=spline(t,y(:,1));spy=spline(t,y(:,2));
%
figure(4);fnplt(spy,[0,5],'r');grid on;
%
[t0,y0]=ginput(1);
t0=4.5;
[tn,yn]=fsolve(@(t)ppval(spy,t),t0,optimset('display','off'));
xmax(i)=ppval(spx,tn);
end;
sp=spline(Al,xmax);figure(4);fnplt(sp,[-pi/2 pi/2],'r');grid on;
[Al0,xmax0]=ginput(1);
[Al,xmax]=fminsearch(@(Al)-ppval(sp,Al),Al0);xmax=-xmax-l;
fprintf(['Goc nem toi uu khi khong co ma sat la:
',num2str(Al*180/pi),...
'do, luc nay no cach tuong: ',num2str(xmax),'m \n']);
% Thoi diem qua bong cham tuong la: 2.0101s luc nay no co do cao:
7.4483m
% Thoi diem qua bong cham dat la: 2.9333s luc nay no cach tuong:
1.3987m
13


% Goc nem toi uu khi co ma sat la: 12.8022do, luc nay no cach
tuong: 2.6113m
% Goc nem toi uu khi khong co ma sat la: 39.3298do, luc nay no cach

tuong: 34.8036m

BÀI 8: TÊN LỬA PHÓNG THẲNG ĐỨNG
function baitoan8
clear all;close all;clc;
syms m vz ve g t dm dvz dt F Dz D2z Dm vth
dvz=D2z*dt;dm=Dm*dt;
F=-m*g-Dz*abs(Dz)*m*g/(vth^2);
p0=m*vz;
p1=(m+dm)*(vz+dvz)-dm*(vz-ve);
dp=p1-p0;
eq=dp/dt-F;
eq=simple(subs(eq));
%neu toc do chay cua nhien lieu là 5m/s
m=dsolve('Dm=-5','m(0)=100','t');Dm=diff(m,t);
t1=solve(m-10,t);t1=double(t1);
fprintf(['thoi gian de nhien lieu chay het
la:',num2str(t1),'s\n']);
% bieu thuc giai tich cua gia toc
a=solve(eq,D2z);a=limit(a,dt,0);
%fprintf(['bieu thuc giai tich cua gia toc la:',char(a),'\n']);
%khi ve=1000m/s; vth=100m/s; g=9.8 m/s^2
ve=1000;vth=100;g=9.8;
a1=subs(a);
a1=subs(a1,Dz,'h(2)');
eqs1=inline(['[','h(2)',';',char(a1),']'],'t','h');
[ti1,h1]=ode45(eqs1,[0,t1],[0 0]);
fprintf(['Do cao khi chay het nhien lieu la:
',num2str(h1(end,1)),'km \n']);
fprintf(['Van toc khi chay het nhien lieu la:

',num2str(h1(end,2)),'m/s\n']);
%sau khi nhien lieu chay het
m=10;Dm=0;
a2=subs(a);
a2=subs(a2,Dz,'h(2)');
eqs2=inline(['[','h(2)',';',char(a2),']'],'t','h');
[ti2,h2]=ode45(eqs2,[t1,120],[h1(end,1) h1(end,2)]);
sp=spline(ti2,h2(:,1));
%thoi diem cham dat và do cao cuc dai
14


tg=fsolve(@(ti2)ppval(ti2,sp),100,optimset('display','off'));
fprintf(['Thoi diem cham dat: ',num2str(tg),'s\n']);
[tmax,hmax]=fminsearch(@(ti2)-ppval(ti2,sp),32);
fprintf(['Do cao cuc dai: ',num2str(-hmax),'m\n']);
% Do thi:
fnplt(sp,[t1,tg],'b');hold on;grid on;
plot(ti1(end),h1(end,1),'ok',ti1,h1(:,1),'r');grid on;hold off;
text(ti1(end),h1(end,1),'Het nhien lieu');
%
%
%
%
%

thoi gian de nhien lieu chay het la:18s
Do cao khi chay het nhien lieu la: 4688.4344km
Van toc khi chay het nhien lieu la: 602.9548m/s
Thoi diem cham dat: 104.8246s

Do cao cuc dai: 6538.0025m

BÀI 9: TÊN LỬA PHÓNG NGHIÊNG GÓC 45 ĐỘ
function baitoan9
clear all;close all;clc;
syms m t v ve dm dt vx vy dvx dvy
syms F Fx Fy Dm D2x D2y vth g k
phi=pi/4;g=9.8;vth=100;ve=1000;v0=10;
k=10*g/(vth^2);v=sqrt(vx^2+vy^2);dvx=D2x*dt;dvy=D2y*dt;dm=Dm*dt;
Fx=-k*v*vx; Fy=-m*g-k*v*vy;
p1x=(m+dm)*(vx+dvx)-dm*(vx-ve*vx/v);p0x=m*vx;
p1y=(m+dm)*(vy+dvy)-dm*(vy-ve*vy/v);p0y=m*vy;
dpx=p1x-p0x;
dpy=p1y-p0y;
eqx=subs(dpx/dt-Fx);
eqy=subs(dpy/dt-Fy);
%khi nhien lieu chay voi toc do khong doi 5kg/s
m=dsolve('Dm=-5','m(0)=100','t');m=subs(m);
Dm=diff(m,t);Dm=subs(Dm);
tg=solve(m-10,t);tg=double(tg);
fprintf(['thoi gian chay het nhien lieu la: ',num2str(tg),'s \n']);
%bieu thuc giai tich cua a
ax=solve(eqx,D2x);ax=limit(ax,dt,0);
ay=solve(eqy,D2y);ay=limit(ay,dt,0);
% a=sqrt(ax^2+ay^2);a=simple(subs(a));
% fprintf(['bieu thuc giai tich cua gia toc: ',char(a),'\n']);
ax1=subs(ax);
ay1=subs(ay);
ax1=subs(ax1,{'vx','vy'},{'u(2)','u(4)'});
ay1=subs(ay1,{'vx','vy'},{'u(2)','u(4)'});

15


eqs=inline(['[','u(2)',';',char(ax1),';','u(4)',';',char(ay1),']'],
't','u');
[t1,u1]=ode45(eqs,[0 tg],[0 (v0*cos(phi)) 0 (v0*sin(phi))]);
fprintf(['tam xa khi chay het nhien lieu la:
',num2str(u1(end,1)),'m \n']);
fprintf(['do cao khi chay het nhien lieu la:
',num2str(u1(end,3)),'m \n']);
fprintf(['van toc khi chay het nhien lieu la:
',num2str(sqrt(u1(end,2)^2+u1(end,4)^2)),'m/s\n']);
%sau khi nhien lieu chay het
m=10;Dm=0;
ax2=subs(ax);
ay2=subs(ay);
ax2=subs(ax2,{'vx','vy'},{'u(2)','u(4)'});
ay2=subs(ay2,{'vx','vy'},{'u(2)','u(4)'});
eqs1=inline(['[','u(2)',';',char(ax2),';','u(4)',';',char(ay2),']']
,'t','u');
[t2,u2]=ode45(eqs1,[tg 31],[u1(end,1) u1(end,2) u1(end,3)
u1(end,4)]);
%thoi diem cham dat, vi tri cham dat va do cao cuc dai
plot([t1; t2],[u1(:,3); u2(:,3)]); grid on; hold on;
plot(t1(end),u1(end,3),'r*');
text(t1(end),u1(end,3),'Het nhien lieu');
spy=spline(t2,u2(:,3));
fun=@(t2)ppval(t2,spy);
[x0 y0]=ginput(1);
tg1=fsolve(fun,x0,optimset('display','off'));

fprintf(['thoi diem cham dat: ',num2str(tg1),'s \n']);
spy=spline(t1,u1(:,3));
fun1=@(t2)-ppval(t2,spy);
[x0 y0]=ginput(1);
[tmax,dc]=fminsearch(fun1,x0,optimset('display','off'));
fprintf(['do cao cuc dai: ',num2str(-dc),'m \n']);
spx=spline(t2,u2(:,1));
xcd=ppval(spx,tg1);
fprintf(['vi tri cham dat: ',num2str(xcd),'m \n']);
%hinh dong
figure(2);
t=[t1;t2];
x=[u1(:,1);u2(:,1)]; x=x(find(t<=tg1));
y=[u1(:,3);u2(:,3)]; y=y(find(t<=tg1));
h1=plot(x(1),y(1),'or');hold on;
h2=plot(x(1),y(1),'.r','markersize',30);
axis([0 12000 0 600]);
for k=1:length(x)
16


set(h1,'xdata',x(1:k),'ydata',y(1:k));
set(h2,'xdata',x(k),'ydata',y(k));
pause(0.1);
end;

%
%
%
%

%
%
%

thoi gian chay het nhien lieu la: 18s
tam xa khi chay het nhien lieu la: 7802.7089m
do cao khi chay het nhien lieu la: 544.4364m
van toc khi chay het nhien lieu la: 712.0285m/s
thoi diem cham dat: 30.7533s
do cao cuc dai: 582.4665m
vi tri cham dat: 10115.3337m

BÀI 10: CHUYỂN ĐỘNG CỦA HÀNH TINH
function baitoan10
clear all;close all;clc;
tn=5;
x0=1;y0=0.3;vx0=0.2;vy0=7;
eq=inline(['[u(2);','-4*pi^2*u(1)/(u(1)^2+u(3)^2)^(3/2);',...
'u(4);','-4*pi^2*u(3)/(u(1)^2+u(3)^2)^(3/2)]'],'t','u');
opt=odeset('reltol',1e-9,'abstol',1e-12);
[t,u]=ode45(eq,0:0.01:tn,[x0 vx0 y0 vy0],opt);
x=u(:,1);y=u(:,3);
vx=u(:,2); vy=u(:,4);
r=sqrt(x.^2+y.^2);
v=sqrt(vx.^2+vy.^2);
%chu ky
plot(t,x,'g',t,r,'r');title('do thi x(t),r(t)');grid
on;legend('x(t)','r(t)');
sp=spline(t,x);
[tn0 xn0]=ginput(2);

[tn1 xn1]=fsolve(@(t)ppval(sp,t),tn0,optimset('display','off'));
T=abs(tn1(1)-tn1(2));
fprintf(['chu ky: ',num2str(T),'year \n']);
%ban truc lon, ban truc nho
sp1=spline(t,r);
[t0min r0min]=ginput(1);
[tmin
rmin]=fminsearch(@(t)ppval(sp1,t),t0min,optimset('display','off'));
[t0max r0max]=ginput(1);
17


[tmax rmax]=fminsearch(@(t)ppval(sp1,t),t0max,optimset('display','off'));
rmax=-rmax;
a=(rmin+rmax)/2;
c=a-rmin;
b=sqrt(a^2-c^2);
fprintf(['ban truc lon la: ',num2str(a),' dvtv \n']);
fprintf(['ban truc nho la: ',num2str(b),' dvtv \n']);
%ve quy dao
figure(2);
plot(x,y,'r');
axis([-2 1.5 -1 2]);grid on;hold on;
plot(0,0,'.r','markersize',50);
% h1=plot(x(1),y(1),'ob');
h2=plot(x(1),y(1),'.b','markersize',30);
pause(0.1);
for i=1:length(x)
%
set(h1,'xdata',x(1:i),'ydata',y(1:i));

set(h2,'xdata',x(i),'ydata',y(i));pause(0.05);
end
%Kiem tra lai dinh luat Kepler III
x0kt=1;y0kt=0;vx0kt=0;vy0kt=5:.5:8;
for k=1:length(vy0kt)
[tkt,ukt]=ode45(eq,0:0.01:tn,[x0kt vx0kt y0kt vy0kt(k)],opt);
xkt=ukt(:,1);ykt=ukt(:,3);
rkt=sqrt(xkt.^2+ykt.^2);
figure(3);
plot(tkt,xkt,'g');title('do thi xkt(t)');grid on;
sp1=spline(tkt,xkt);
[tn01 xn01]=ginput(2);
[tn2
xn2]=fsolve(@(tkt)ppval(tkt,sp1),tn01,optimset('display','off'));
Tkt=abs(tn2(1)-tn2(2));
akt=(max(rkt)+min(rkt))/2;
Ts(k)=(Tkt^2)/(akt^3);
end
fprintf(['ket qua kiem tra ti so T^2/a^3 = \n',num2str(Ts),'\n']);
%
%
%
%
%

chu ky: 1.8094year
ban truc lon la: 1.4849 dvtv
ban truc nho la: 1.3459 dvtv
ket qua kiem tra ti so T^2/a^3 =
0.99998

0.99978
1
1
18

1

1

1


BÀI 11: CON LẮC ĐƠN
function baitoan11
close all;clear all;clc;
syms g l b
g0=9.8;l0=3;b1=0;b2=0.1/3;
eq='-g/l*sin(u(1))-b*l^2*abs(u(2))*u(2)';
%truong hop ko co ma sat
eq1=char(subs(eq,{g,l,b},{g0,l0,b1}));
eq1=inline(['[u(2);',eq1,']'],'t','u');
[t1,u1]=ode45(eq1,[0:0.05:30],[pi/3 0]);
teta1=u1(:,1);dteta1=u1(:,2);
x1=l0*sin(teta1);y1=l0*(1-cos(teta1));
Ed1=1./2*(l0*dteta1).^2;Et1=g0*l0*(1-cos(teta1));
E1=Ed1+Et1;
% truong hop co ma sat
eq2=char(subs(eq,{g,l,b},{g0,l0,b2}));
eq2=inline(['[u(2);',eq2,']'],'t','u');
[t2,u2]=ode45(eq2,[0:0.05:30],[pi/3 0]);

teta2=u2(:,1);dteta2=u2(:,2);
x2=l0*sin(teta2);y2=l0*(1-cos(teta2));
Ed2=1./2*(l0*dteta2).^2;Et2=g0*l0*(1-cos(teta2));
E2=Ed2+Et2;
%cac do thi
figure(1);
subplot(2,1,1);
plot(t1,teta1,t1,dteta1,'r');grid on;
legend('teta(t)','d(teta(t))/dt');
title('khi khong co ma sat - dao dong dieu hoa');
subplot(2,1,2);
plot(t2,teta2,t2,dteta2,'r');grid on;
legend('teta(t)','d(teta(t))/dt');
title('khi co ma sat - dao dong tat dan');
figure(2);
subplot(2,1,1);
plot(t1,Ed1,t1,Et1,'r',t1,E1,'g');grid on;
legend('dong nang (t)','the nang(t)','tong nang luong(t)');
title('khi khong co ma sat - nang luong bao toan');
subplot(2,1,2);
plot(t2,Ed2,t2,Et2,'r',t2,E2,'g');grid on;
legend('dong nang (t)','the nang(t)','tong nang luong(t)');
title('khi co ma sat - nang luong khong bao toan');
figure(3); %khong gian pha
plot(teta1,dteta1,teta2,dteta2,'r');grid on;
19


legend('khong co ma sat','co ma sat');
title('khong gian pha');

%su phu thuoc cua chu ki vao goc teta khi khong co ma sat
teta0=pi/18:pi/9:pi/2; u0=[teta0(:) zeros(size(teta0(:)))];
for k=1:length(teta0)
[t3,u3]=ode45(eq1,[0:0.05:10],u0(k,:));
teta3=u3(:,1);
figure(4);
plot(t3,teta3);grid on;
sp=spline(t3,teta3);
[t30 teta30]=ginput(2);
[t3n,teta3n]=fsolve(@(t3)ppval(sp,t3),t30,optimset('display','off')
);
T(k)=abs(t3n(1)-t3n(2));
end
fprintf('bang phu thuoc cua chu ky vao teta :\n');
disp([T(:) teta0(:)]);
Tb=2*pi*sqrt(l0/g0)*ones(size(teta0(:)));
figure(4);
plot(teta0,T,teta0,Tb,'r');grid on;title('su phu thuoc cua chu ky
vao teta');
legend('khi goc lon','khi goc be');xlabel('teta');ylabel('chu ky');
%hinh dong
figure(5);
plot([0,0],[l0 1.1*l0],'g','linewidth',10); %ve diem treo
title('khi khong co ma sat - dao dong tuan hoan');
hold on;axis equal;axis(l0*[-1.1 1.1 -1.1 1.1]);
h1=plot([0 x1(1)],[l0 y1(1)],'linewidth',2); %ve day treo
h2=plot(x1(1),y1(1),'.r','markersize',30);
%ve qua lac
pause(.4);
for k=1:length(x1)

x=[0 x1(k)];y=[l0 y1(k)];
set(h1,'xdata',x,'ydata',y);
set(h2,'xdata',x1(k),'ydata',y1(k));pause(0.03);
end
figure(6);
plot([0,0],[l0 1.1*l0],'k','linewidth',10);
title('khi co ma sat - dao dong tat dan');
hold on;axis equal;axis(l0*[-1.1 1.1 -1.1 1.1]);
h3=plot([0 x2(1)],[l0 y2(1)],'linewidth',2);
h4=plot(x2(1),y2(1),'.y','markersize',30);
pause(.4);
for k=1:length(x2)
x=[0 x2(k)];y=[l0 y2(k)];
20


set(h3,'xdata',x,'ydata',y);
set(h4,'xdata',x2(k),'ydata',y2(k));pause(0.03);
end
% bang phu thuoc cua chu ky vao teta :
%
3.4826
0.1745
%
3.5361
0.5236
%
3.6480
0.8727
%

3.8279
1.2217
%
4.1015
1.5708

BÀI 12: DAO ĐỘNG CƯỠNG BỨC
function baitoan12
close all;clear;clc;
syms x w0 w1 k t ti
w0=1.5;w1=1.9;k=0.2;ti=0:0.1:60;
sol=dsolve('D2x=-w0^2*x-k*Dx-cos(w1*t)','x(0)=0,Dx(0)=0','t');
x=subs(sol);xi=real(double(subs(x,t,ti)));
vx=diff(x,t);vxi=real(double(subs(vx,t,ti)));
Edi=1/2*vxi.^2;Eti=1/2*w0^2*xi.^2;
Ei=Edi+Eti;
figure(1);
plot(xi,vxi);grid on;
title('khong gian pha');
figure(2);
subplot(2,1,1);
plot(ti,Edi,ti,Eti,ti,Ei);grid on;
legend('Edi','Eti','Ei');
subplot(2,1,2);
plot(ti,xi,ti,vxi);grid on;
legend('xi(t)','vxi(t)');
%khi bien do on dinh
figure(3);
plot(ti,vxi);grid on;
title('van toc dao dong cuong buc theo thoi gian');

fvx=inline(vectorize(vx),'t');
[t0,v0]=ginput(1);
[tn,vn]=fsolve(fvx,t0,optimset('display','off'));
Atn=abs(double(subs(x,t,tn)));
Alt=1/sqrt((w1^2-w0^2)^2+k^2*w1^2);
disp('Bien do khi on dinh theo thuc nghiem va ly
thuyet');disp([Atn,Alt]);
%Su phu thuoc cua bien do dao dong khi on dinh vao tan so ngoai luc
w1
21


w12=1.2:0.1:1.8;
for i=1:length(w12)
w1=w12(i);
x=subs(sol);
xi=double(subs(x,t,ti));
vx=diff(x,t);
vxi=real(double(subs(vx,t,ti)));
figure(4);
plot(ti,vxi);grid on;
fvx=inline(vectorize(vx),'t');
[t0,v0]=ginput(1);
[tn,vn]=fsolve(fvx,t0,optimset('display','off'));
Atn(i)=abs(double(subs(x,t,tn)));
Alt(i)=1/sqrt((w1^2-w0^2)^2+k^2*w1^2);
end
disp('Bang phu thuoc A vao w1');
disp('
w1

thuc nghiem
ly thuyet');
disp([w12(:),Atn(:),Alt(:)]);
plot(w12(:),Atn(:),'-r+',w12(:),Alt(:),'-bo');
legend('thuc nghiem','ly thuyet');
% Bien do khi on dinh theo thuc nghiem va ly thuyet
%
0.6771
0.7082
%
% Bang phu thuoc A vao w1
%
w1
thuc nghiem ly thuyet
%
1.2000
1.1860
1.1837
%
1.3000
1.5715
1.6197
%
1.4000
2.5094
2.4807
%
1.5000
3.3037
3.3333

%
1.6000
2.2472
2.2445
%
1.7000
1.3949
1.3799
%
1.8000
0.9391
0.9493

BÀI 13: HỆ GỒM 50 DAO ĐỘNG TỬ TUYẾN TÍNH
function baitoan13
close all;clear all;clc;
global L k m we b uj vj j ti t1
L=50; m=1; k=1; we=1; b=0.1; j=1:L; ti=0:0.1:100;
u0=[zeros(size(j)) zeros(size(j))];
[t1,u1]=ode45('hpt_13',ti,u0);
uj=u1(:,1:2:2*L-1);
vj=u1(:,2:2:2*L);
l=[5 20 45];
22


for a=1:length(l)
subplot(3,1,a);
plot(ti,uj(:,l(a)),'-');grid on;
title(['li do cua dao dong tu thu ' num2str(l(a))]);

end
%%%%PHAN B:
figure(2);
tj=[5 20 100];
for i=1:length(tj)
n=find(ti==tj(i));
subplot(3,1,i);
plot(j,uj(n,:));
grid on;
title(['Li do cua he dao dong tai thoi diem t = ',
num2str(tj(i))]);
end

====================
function du=hpt_13(t,u)
global k m we b L
du(1)=u(2);du(2)=-k/m*(2*u(1)-u(3))-b*u(2)/m + 0.5*cos(we*t)/m;
for j=2:L-1
du(2*j-1)=u(2*j);
du(2*j)=-k/m*(2*u(2*j-1)-u(2*j-3)-u(2*j+1))-b*u(2*j)/m;
end
du(2*L-1)=u(2*L);
du(2*L)=-k/m*(2*u(2*L-1)-u(2*L-3))-b*u(2*L)/m;
du=du(:);

BÀI 14: NHIỄU XẠ
function baitoan14
clc;clear all;close all;
L=200;lm=600*1e-9;A=1;q=2*pi/lm;
while 1

k1=menu('Nhieu xa: ','n khe','lo tron','vanh tron','thoat');
switch k1
case 1%nhieu xa khe thuc
n=input('nhap so khe nhieu xa :')
D=5*lm;
a=25*lm;
q=2*pi/lm;
M=21;
d=D/(M-1);%chia moi khe thuc thanh nhieu khe nho
c=0;
y=-20:0.1:20;
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yl=[-(n-1)/2:(n-1)/2].*a;
for nn=1:length(yl)
yk1=[-(M-1)/2:(M-1)/2].*d+repmat(yl(nn),1,M);
yk(:,nn)=yk1(:);
end;yk=yk(:);
rrk=inline('sqrt((y-yk).^2+L^2)','y','yk','L');
for k=1:length(yk)
c=c+A./rrk(y,yk(k),L).*exp(-i*q*rrk(y,yk(k),L));
end
I=abs(c.^2);
Imax=max(I);
I=I/Imax;
II=repmat(I,2,1);
figure;
subplot(2,1,1);
plot(y,I);

xlabel('mm');
subplot(2,1,2);
pcolor(y,1:2,II);
mau=gray;mau(:,[3])=0;
set(gcf,'colormap',mau);
shading interp;shg;xlabel('mm');
case 2 %Nhieu xa lo tron
R=5*lm;dn=R/50;
Rm=50;dm=Rm/100;
[xk,yk]=meshgrid(-R:dn:R);
xk=xk(:);
yk=yk(:);
k=find((xk.^2+yk.^2)xk=xk(k);
yk=yk(k);
rrk=inline('sqrt(yk.^2+(xxk).^2+L^2)','x','xk','yk','L');
x=0:dm:Rm;c=zeros(size(x));
for k=1:length(xk)
c=c+A./rrk(x,xk(k),yk(k),L).*exp(i*q*rrk(x,xk(k),yk(k),L));
end;
I=abs(c.^2);
Imax=max(I);
I=I/Imax;
II=[fliplr(I) I(2:end)];
figure;
x1=-Rm:dm:Rm;
plot(x1,II);
24

xlabel('mm');
[r,p]=meshgrid(0:dm:Rm,0:pi/30:2*pi);
x=r.*cos(p);
y=r.*sin(p);
I=repmat(I,size(x,1),1);
figure;pcolor(x,y,I);
mau=gray;
mau(:,[3])=0;
set(gcf,'colormap',mau);
shading interp;axis square;
case 3 % Vanh tron
R=7*lm;
dn=R/50;
Rm=50;
dm=Rm/100;
[xk,yk]=meshgrid(-R:dn:R);
xk=xk(:);
yk=yk(:);
k=find((((xk).^2+(yk).^2)<(7*lm)^2)&(((xk).^2+(yk).^2)>(5*lm)^2));
xk=xk(k);
yk=yk(k);
rrk=inline('sqrt(yk.^2+(xxk).^2+L^2)','x','xk','yk','L');
x=0:dm:Rm;c=zeros(size(x));
for k=1:length(xk)
c=c+A./rrk(x,xk(k),yk(k),L).*exp(i*q*rrk(x,xk(k),yk(k),L));
end;
I=abs(c.^2);
Imax=max(I);
I=I/Imax;
II=[fliplr(I) I(2:end)];

figure;
x1=-Rm:dm:Rm;
plot(x1,II);
xlabel('mm');
[r,p]=meshgrid(0:dm:Rm,0:pi/30:2*pi);
x=r.*cos(p);
y=r.*sin(p);
I=repmat(I,size(x,1),1);
figure;
pcolor(x,y,I);
mau=gray;
mau(:,[3])=0;
25