ví dụ mathlab cơ bản

CÁC BÀI TOÁN NGUỘI CỦA CỐC CAFEVD1: Xac dinh các tham so trong qua trinh nguoi cua coc cafe den bang phuong phap xap xi ham phi tuyen... VD5: Mo phong Monte-Callor quy luat phan huy hat

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CÁC BÀI TOÁN NGUỘI CỦA CỐC CAFE

VD1: Xac dinh các tham so trong qua trinh nguoi cua coc cafe den bang phuong

phap xap xi ham phi tuyen

Phuong trinh : dT/dt=-r(T-Tf)

-o0o -% Gan so lieu

clc;clear all;close all;

ti=0:2:46; % Thoi gian do

nTf=17; % Nhiet do phong

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 ]; % Nhiet do thuc nghiem

% Giai phuong trinh nguoi

T=dsolve('DT=-r*(T-Tf)','T(0)=T0','t');

disp('Bieu thuc T tinh duoc:'); pretty(T)

%Tinh gia tri va ve do thi cua coc cafe den

title('Qua trinh nguoi cua coc cafe den');

xlabel('Thoi gian(phut)'); ylabel('Nhiet do (C)');

legend('So lieu tinh','So lieu do');

Qua trinh nguoi cua coc cafe den

VD2: Xac dinh cac tham so trong qua trinh nguoi cua coc cafe den bang xap xi

ham phi tuyen

Phuong trinh : dT/dt=-r(T-Tf)^2 -o0o -

% Gan so lieuclc;clear all;close all;ti=0:2:46; % Thoi gian donTf=17; % Nhiet do phongTcd=[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

% Giai phuong trinh nguoiT=dsolve('DT=-r*(T-Tf)^2','T(0)=T0','t'); %Tim no giai tich cua ptvp thuongdisp('Bieu thuc T tinh duoc:'); pretty(T)

%pretty:Bieu dien dang tu nhien cua bien sym

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%Tinh gia tri va ve do thi cua coc cafe den

title('Qua trinh nguoi cua coc cafe den');

xlabel('Thoi gian(phut)'); ylabel('Nhiet do (C)');

62.5 60.1 58.1 56.1 54.3 52.8

51.2 49.9 48.6 47.2 46.1 45.0

% Giai phuong trinh nguoiT=dsolve('DT=-r(2)*(T-Tf)^2-r(1)*(T-Tf)','T(0)=T0','t');

%Tinh gia tri va ve do thi cua coc cafe densyms r1r2

T12=subs(T,{'r(1)','r(2)'},{r1,r2});

disp('T12='); pretty(T12)T1=limit(T12,r2,0);

disp('T1='); pretty(T1)

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T2=limit(T12,r1,0); %Tinh gioi han cua T12

plot(ti,Tcd,'o',ti,(f(r1201,ti)),'.-');

title('Mo hinh dT/dt=-r_1.(T-Tf)');

xlabel('t-min'); ylabel('T (C)'); grid on;

figure(2);

title('Mo hinh dT/dt=-r_2.(T-Tf)^2');

figure(3);

title('Mo hinh dT/dt=-r_1.(T-Tf)-r_2.(T-Tf)^2');

% -End -r12 = 0.0074 0.0004

35 40 45 50 55 60 65 70 75 80 85

%Tinh gia tri va ve do thi cua coc cafe densyms rT0TfPt

plot(ti,Tcd,'o',ti,(f(Pn,ti)),'.-');

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title('Mo hinh dT/dt=-r_1.(T-Tf)');

% Giai phuong trinh nguoi dT/dt=-r2(T-Tf)^2

plot(ti,Tcd,'o',ti,(f(Pn,ti)),'.-');

title('Mo hinh dT/dt=-r_2.(T-Tf)^2');

% -End -0 5 10 15 20 25 30 35 40 45 50 35

40 45 50 55 60 65 70 75 80 85

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CÁC BÀI TOÁN PHÂN HỦY HẠT NHÂN

VD1:

-o0o -function box1;

close all; clc;

N=1000; dt=N/10; t=0:10*N; % N-so hat trong hop

n=zeros(size(t)); n(1)=N; %Tao mang co kich thuoc t co cac ptu =0

400 500 600 700 800 900

1000

ngiai tichN/2 n

mo phong

VD2:

function nucdecay1;

-o0o -clc;clear all;close all;

% Mo phong Monte-Callor quy luat phan huy hat nhan

% theo phan bo Poisson

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global ntrial; figure(fig);

n=0:max(nn); np=hist(nn,n); Pi=np/ntrial; %hist=>tinh tan so cua mau

m=mean(nn); s2=var(nn);

subplot(2,1,1); bar(n,np); xlim([0 n(end)]);

title(['Tan so phan huy sau ',

hold on; plot(n,Plt,'.r-'); hold off;

title(['Phan bo Poisson voi < n > = ',

num2str(m)])

0 500 1000 1500 2000

Tan so phan huy sau 1 dvtg

0 0.05 0.1 0.15 0.2

Phan bo Poisson voi < n > = 5.0085

0 500 1000

1500

Tan so phan huy sau 2 dvtg

0 0.05 0.1 0.15 0.2

Phan bo Poisson voi < n > = 9.9415

VD3: Mo phong Monte-Callor phan huy hat nhan

clear; clc; close all;

-o0o -N0=10; % N0 -So hat nhan khong ben luc daup=0.01; % p -Xac suat phan huy

tmax=500; % tmax -Khoang thoi gian khao satntrial=200; % ntrial -So lan thu

ti=1:tmax; ncum=zeros(1,tmax);

for k=1:ntrial N=ones(1,N0);

ti=[0 ti]; ni=[N0 ni];

ni_gt=N0*exp(-p*ti);

h=plot(ti(1),ni(1),'r',ti,ni_gt,'b');

legend('ni_{mo phong}','ni_{giai tich}');

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-o0o -clear; clc; close all;

N0=5000; % -So hat nhan khong ben luc dau

p1=0.01; % -Xac suat phan huy h/n ng/to 1

p2=0.005; % -Xac suat phan huy h/n ng/to 2

% tmax: -Khoang thoi gian khao sat

% ntrial: -So lan thu

ncum1(t)=ncum1(t)+sum(N1);

ncum2(t)=ncum2(t)+sum(N2);

endendni1=ncum1/ntrial;

5000

n1i

mphong

n1igtichn2imphongn2igtich

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VD5: Mo phong Monte-Callor quy luat phan huy hat nhan

Theo quy luat ham mu

-o0o -clc; close all;

N0=2000; % N0-So hat nhan khg ben luc dau

p=0.01; % p-Xac suat phan huy

tmax=200; % khoang thoi gian quan sat

ntrial=1; % ntrial-So lan thu

ti=[0 ti]; ni=[N0 ni];

ni_gt=N0*exp(-p*ti); %Cong thuc giai tich

VD6: Mo phong Monte-Callor quy luat phan huy hat nhan

Ngto pxa 1(me) > ngto pxa 2(con) Khi bi pra >ngto ben vung -o0o -clc; close all; close all;

N0=2000; % N0-So hat nhan khg ben luc daup1=0.01; % Xac suat phan huy hat nhan gto 1(me)p2=0.005; % Xac suat phan huy hat nhan gto 2(con)tmax=500; % khoang thoi gian quan sat

ntrial=1; % ntrial-So lan thuti=1:tmax;

ncum1=zeros(1,tmax);

ncum2=ncum1;

for k=1:ntrial N1=ones(1,N0);

N2=zeros(1,N0);

for t=1:tmax r1=rand(size(N1));

r2=rand(size(N2));

N3=N1&(r1<=p1); %So hat nhan me bi phan huy thanh hat nhan con N1=N1&(r1>p1); %So hat nhan me ko bi phan huy thanh hat nhan con N2=N2&(r2>p2); %So hat nhan con ko bi phan huy

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ti=[0 ti]; ni1=[N0 ni1];ni2=[N0 ni2];

ni1_gt=N0*exp(-p1*ti); %Cong thuc giai tich

ni2_gt=N0/(p1-p2)*p1*exp(-p2*ti)-N0/(p1-p2)*p1*exp(-p1*ti);

plot(ti,ni1,'r',ti,ni1_gt,'b',ti,ni2,'k',ti,ni2_gt,'g');

legend('n1i_{mo phong}','n1i_{giai tich}','n2i_{mo phong}','n2i_{giai tich}');

0 200 400 600 800 1000

eqs=[eq1,',',eq2,',',eq3];

ints='NKr(0)=1,NBr(0)=0,NSe(0)=0'; %Dieu kien ban daudsol=dsolve(eqs,ints);

title('Qua trinh phan huy phong xa nguyen to Kr');

xlabel('Thoi gian/h'); ylabel('Khoi luong/mg')

% -End -0 20 40 60 80 100 120 140 160 180 200 0

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

CÁC BÀI TOÁN CHUYỂN ĐỘNG

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VD1: Qua bong nem xien 40 do

subplot(2,1,1); ezplot(x1,y1,[0 tn]); title('Quy dao y(x)'); grid on;pause;

% % Hinh anh chuyen dong -

-End -10

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t y1(t)

t Vy1(t)

c=menu('Chon :','Nhap Vth','Hinh ch/dg');

switch c case 1nvt=input('Nhap van toc toi han vt=');

xlim([-.2 9]); xlabel('t-Thoi gian (s)');

ylabel('y-Vi tri (m)');

title('Qua cau xop roi co tinh den ma sat');

case 2 disp(['Van toc Vt2=',num2str(nvt)]) break;

endend

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% Van toc va gia toc

-figure(2);

subplot(1,2,1); plot(ti,vy,'.-');

ylabel('Vy-Van toc (m/s)');

pp=spline(ti,vy);

pp1=fnder(pp); %Dao ham he da thuc bac n

subplot(1,2,2); plot(ti,ppval(pp1,ti),'.-');

ylabel('Ay-Gia toc (m/s^2)');

-End -0.2 -0.1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 -3.5

-3 -2.5 -2 -1.5 -1 -0.5 0

-6 -5 -4 -3 -2 -1 0

-9 -8 -7 -6 -5 -4 -3 -2

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clear all; close all; clc

% Chu y khi k1=10,k1=0 bieu thuc suy bien

% Nen dung ham limit thay ham subs

for k=1:4 ve=vek(k); cl=clk(k);

z2=subs(z1); z2=subs(z2,t,gtt);

vz2=subs(vz1); vz2=subs(vz2,t,gtt);

subplot(2,2,1); plot(gtt,z2,cl); hold on; title('Do thi z(t)'); grid on; subplot(2,2,3); plot(gtt,vz2,cl); hold on; title('Do thi Vz(t)'); grid on; subplot(1,2,2);plot(z2,vz2,cl);hold on; title('Do thi Vz(z)'); grid on; lg{k}=(['ve=',num2str(ve)]);

endlegend(lg);

% d Truong hop khi Fms=k2*Dz^2D2z=solve(pt32,D2z);

dz1=inline(['[z(2);',char(D2z1),']'],'t','z');

[t,z]=ode45(dz1,[0 double(tf1)],[0 0]);

subplot(2,2,1); plot(t,z(:,1),clk(k)); hold on; title('Do thi z(t)'); grid on; subplot(2,2,3); plot(t,z(:,2),clk(k)); hold on; title('Do thi Vz(t)'); grid on; subplot(1,2,2); plot(z(:,1),z(:,2),clk(k)); hold on; title('Do thi Vz(z)'); grid on; lg{k}=(['ve=',num2str(vek(k))]);

endlegend(lg);

-End -13

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0 200 400 600 800 1000

1200

Do thi Vz(z)

ve=100 ve=200 ve=300 ve=400

0 100 200 300 400 500

600

Do thi Vz(z)

ve=100 ve=200 ve=300 ve=400

VD4: Chuyen dong cua cac hanh tinh

function planet1

-o0o -%Program planetclose all;clc;

%Lz=x.*vy-y.*vx; % ======Mo men dg lg/m: Lz/m=x*vy-y*vx

%====================Bieu dien do thilim=1.2*[min(x),max(x),min(y),max(y)];

figure(1);

plot(x,y,vx,vy); grid on; axis equal; title('Quy dao hanh tinh');

xlabel('x, vx'); ylabel('y, vy'); legend('Toa do','Van toc');

figure(2);

subplot(2,1,1); plot(t,x,t,y,t,r); legend('x(t)','y(t)','r(t)'); xlabel('t'); grid on

subplot(2,1,2); plot(t,vx,t,vy,t,v); legend('vx(t)','vy(t)','v(t)'); xlabel('t'); grid on

figure(3);

subplot(2,1,1); plot(t,r,t,v,t,phi); legend('r(t)','v(t)','phi(t)'); xlabel('t'); grid on

subplot(2,1,2); plot(t,Ek,t,Eu,t,E,t,Lz); legend('Ek(t)','Eu(t)','E(t)','Lz(t)');

14

-2 -1 0 1 2 3 4 5 6 7

Quy dao hanh tinh

Toa do Van toc

-5 0 5 10

t

r(t) v(t) phi(t)

-40 -20 0 20 40

t

Ek(t) Eu(t) E(t) Lz(t)

-2 -1.5 -1 -0.5 0 0.5 1 1.5 2

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set(h(2),'erase','non');

set(h(3),'markersize',50);

axis equal; axis(lim);

xlabel('x'); ylabel('y');

-o0o -%Program planeclear all; close all; clc;

Lz=x.*vy-y.*vx; % -<Mo men xung luong>/m: Lz=x*vy-y*vx

% -Bieu dien do thilim=1.2*[min(x),max(x),min(y),max(y)];

-2 0 2 4 6

Toa do Van toc

-4 -2 0 2 4

x(t) y(t) r(t)

-10 -5 0 5

10

vx(t) vy(t) v(t)

-4 -2 0 2 4

t

x(t) y(t) r(t)

-10 -5 0 5 10

t

vx(t) vy(t) v(t)

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figure(1); shg

plot(x,y,vx,vy); grid on; axis equal; legend('Toa do','Van toc');

figure(2);

subplot(2,1,1); plot(t,x,t,y,t,r); legend('x(t)','y(t)','r(t)'); grid on

subplot(2,1,2); plot(t,vx,t,vy,t,v); legend('vx(t)','vy(t)','v(t)'); grid on

figure(3);

subplot(2,1,1); plot(t,Ek,t,Eu,t,E); legend('Ek(t)','Eu(t)','E(t)'); grid on

subplot(2,1,2); plot(t,E,t,Lz); legend('E(t)','Lz(t)'); grid on

% -Hinh anh chuyen dong

set(h(1),'erase','xor','markersize',20);

set(h(2),'erase','non');

-o0o -clc; clear all; close all;global GM Gm1 Gm2; % GM=G*M; Gm1=G*m1; Gm2=G*m2;

GM1=4*pi^2; dt=.01;

k=menu('Chon:','He mat troi 1','He mat troi 2','Thoat');

switch k case 1GM=GM1;

16

-40 -20 0 20

40

Ek (t) Eu(t) E(t)

-10 -5 0 5

10

E(t) Lz(t)

-3.5 -3 -2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5

Trang 17

axis equal;axis([-4 4 -4 4]);

title('He "Nhat tam"'); xlabel('x'); ylabel('y');

h1=plot(xi(1),yi(1),':g',xi(2),yi(2),':b');

figure(2);

plot(0,0,'.b','markersize',20); hold on;

h2=plot(xi(1)-xi(2),yi(1)-yi(2),'.g',-xi(2),-yi(2),'.r');

axis equal; axis([-4 4 -4 4]);

title('He "Dia tam"'); xlabel('x'); ylabel('y');

set(h(1),'xdat',xi(1),'ydat',yi(1));

set(h(2),'xdat',xi(2),'ydat',yi(2));

set(h1(1),'xdat',x(:,1),'ydat',y(:,1));

set(h1(2),'xdat',x(:,2),'ydat',y(:,2));

set(h2(1),'xdat',xi1(1),'ydat',yi1(1));

set(h2(2),'xdat',xi1(2),'ydat',yi1(2));

set(h3(1),'xdat',x1(:,1),'ydat',y1(:,1));

set(h3(2),'xdat',x1(:,2),'ydat',y1(:,2));

pause(.01);

end;

function [xi,yi,vxi,vyi]=tinh(x0,y0,vx0,vy0,dt);opt=odeset('reltol',1e-3,'abstol',1e-4);

% -u0=[x0(:); y0(:); vx0(:); vy0(:)];

% -global GM Gm1 Gm2r1=sqrt(u(1)^2+u(3)^2);

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-GM*u(2)/r2^3-Gm1*(u(2)-u(1))/r12^3;

-GM*u(3)/r1^3-Gm2*(u(3)-u(4))/r12^3;

-GM*u(4)/r2^3-Gm1*(u(4)-u(3))/r12^3];

-End -CÁC BÀI TOÁN DAO ĐỘNG

VD1: Dao dong dieu hoa

Ko co ngoai luc -o0o -function daodgtdh0;

% Program dao dong tu tuyen tinh

% khong co ngoai lucclc;close all

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% Truong hop rieng voi cac tham so cu the

% - Khong ma sat, dao dong bao toan

% - Co ma sat, dao dong tat dan

-gtri2={gtw 0 1 0 0.2};% gia tri tham so

subplot(2,1,1); plot(t1,gtx1,t1,gtv1); grid on;

title('Dao dong dieu hoa'); legend('x(t)','v(t)');

subplot(2,1,2); plot(t1,gtx2,t1,gtv2); grid on;

title('Dao dong tat dan'); legend('x(t)','v(t)');

% The nang,dong nang va nang luong tong

-plot(gtx1,gtv1,gtx2,gtv2); grid on; xlabel('x'); ylabel('v');

legend('Dieu hoa','Tat dan'); title('Dao dong trong khong gian pha');

% Hinh anh chuyen dong figure(4);

-subplot(2,1,1); chdgdh(gtx1); %goi ham chdgdhsubplot(2,1,2); chdgdh(gtx2);

function chdgdh(x0);

% -plot([-4 -4],[3 0],'linewidth',6); grid on; hold on; xlim([-4 4]);

t=linspace(-pi,10*pi,200);

xx=.25*cos(t)-3.25+(2+x0(1))*(t+pi)/(11*pi);

x=[-4 xx (xx(end)+.52)];

y=.5*[1 sin(t)+1 1];

h1=plot(x,y,'linewidth',3,'erase','xor');

h2=plot(x0(1),.5,'s','markersize',47,'markerfacecolor','r','erase','xor');

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0 1 2

3

Dao dong dieu hoa

Ep(t) Ek(t) Et(t)

0 1 2

3

Dao dong tat dan

Ep(t) Ek(t) Et(t)

-2 -1.5 -1 -0.5 0 0.5 1 1.5 2

x

Dao dong trong khong gian pha

Dieu hoa Tat dan

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Trang 21

VD2: Program dao dong tu dieu hoa

Ep1=gtw^2*gtx1.^2/2; %Dong nang

Ek1=gtv1.^2/2; % The nangEt1=Ep1+Ek1; % Nang luong

% Co ma sat gtri2={gtw gtw1 0 0 0.2 5};

-x2=subs(x,{w,w1,x0,v0,b,c},gtri2); x2=simple(x2)v2=subs(v,{w,w1,x0,v0,b,c},gtri2); v2=simple(v2)fx2=inline(vectorize(x2),'t'); gtx2=fx2(t1);

fv2=inline(vectorize(v2),'t'); gtv2=fv2(t1);

Ep2=gtw^2*gtx2.^2/2; %Dong nangEk2=gtv2.^2/2; % The nang

Et2=Ep2+Ek2; % Nang luong

% Bieu dien do thi

% Ly do, van toc figure(1);

-subplot(2,1,1); plot(t1,gtx1,t1,gtv1); grid on;legend('x(t)','v(t)'); title('Dao dong co ngoai luc khg ma sat');

subplot(2,1,2); plot(t1,gtx2,t1,gtv2); grid on

legend('x(t)','v(t)'); title('Dao dong co ngoai luc co ma sat');

% The nang,dong nang va nang luong tong figure(2);

subplot(2,1,1); plot(t1,Ep1,t1,Ek1,t1,Et1); grid on; legend('Ep(t)','Ek(t)','Et(t)'); title('Dao dong dieu hoa');

subplot(2,1,2); plot(t1,Ep2,t1,Ek2,t1,Et2); grid on;legend('Ep(t)','Ek(t)','Et(t)'); title('Dao dong tat dan');

% Khong gian pha figure(3);

-plot(gtx1,gtv1,gtx2,gtv2); grid on; xlabel('x');ylabel('v');

legend('Khong ma sat','Co ma sat'); title('Dao dong co ng/luc trg khg gian pha');end %while

-End -21

-1 -0.5 0 0.5 1

Dao dong co ngoai luc khg ma sat

-1 -0.5 0 0.5 1

Dao dong co ngoai luc co ma sat

x(t) v(t)

0 0.2 0.4 0.6 0.8

Dao dong dieu hoa

0 0.2 0.4 0.6 0.8

Dao dong tat dan

Ep(t) Ek(t) Et(t)

Trang 22

%Tham so xac dinha1=1.5; w1=1.8; phi1=3;

a2=1.3; w2=1.5; phi2=2;

k=1; k1=1; x=0; y=0; t=0; dt=0.1; p=.03;

%Tao cua so dieu khien va cac phim dieu khienuicontrol('position',[20 20 60 20],

'string','Thoat','callback','k=0;k1=0;')

%unicontrol=>tao giao dien ng/dung de dieu khien doi tuonguicontrol('position',[20 50 60 20],

'string','Dung','callback','k1=1;')uicontrol('position',[20 80 60 20],

'string','Chay','callback','k1=0;')h=plot(x,y,'g','linewidth',2); grid on; axis equal;axis([-2.2 2.2 -2.2 2.2]); set(gca,'color',[0 3 0]);

title('Tong hop 2 dao dong dieu hoa vuong goc');

%Trang thai dung ban dauwhile k1; pause(0.1); end;

%Bat dau chayx=a1*sin(w1*t+phi1); y=a2*sin(w2*t+phi2);

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-2 -1.5 -1 -0.5 0 0.5 1 1.5 2 -2

-1.5 -1 -0.5 0 0.5 1 1.5 2 Tong hop 2 dao dong dieu hoa vuong goc

VD4: Chuong trinh he 2 dao dong tu dieu hoa

subplot(2,1,1); ezplot(x13,[0 30]); grid on;title('Do thi x1(t) khi Dkd phuc tap');

subplot(2,1,2); ezplot(x23,[0 30]); grid on;title('Do thi x2(t) khi Dkd phuc tap');

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Do thi x2(t) khi Dkd phuc tap

VD5: Con lac phi tuyen

function conlacphituyen

-o0o -% Program dao dong con lac phi tuyen

% khong co ngoai lucclc;close all

% - Co ma sat, dao dong tat dan sm0=subs(st0,{g,L,b},{g0,L0,b2});

Trang 25

% Bieu dien do thi

% - Goc, van toc goc

-figure(1);

subplot(2,1,1); plot(t1,th1,t1,dth1); grid on;

legend('\theta(t)','\theta''(t)'); title('Dao dong bao toan');

subplot(2,1,2); plot(t1,th2,t1,dth2); grid on;

legend('\theta(t)','\theta''(t)'); title('Dao dong tat dan');

% - The nang,dong nang va nang luong tong

figure(2);

subplot(2,1,1);plot(t1,Ep1,t1,Ek1,t1,Et1); grid on;

legend('Ep(t)','Ek(t)','Et(t)'); title('Dao dong bao toan');

subplot(2,1,2); plot(t1,Ep2,t1,Ek2,t1,Et2); grid on;

legend('Ep(t)','Ek(t)','Et(t)'); title('Dao dong tat dan');

% - Khong gian pha

-figure(3);

plot(th1,dth1,th2,dth2); grid on; xlabel('\theta'); ylabel('\theta''');

legend('Bao toan','Tat dan'); title('Dao dong trong khong gian pha');

% % - Hinh anh chuyen dong

VD6: Con lac kép

function conlackep

-o0o -25

-4 -2 0 2 4

Dao dong bao toan

-4 -2 0 2

Dao dong tat dan

0 2 4 6 8 10 12 14 16 18 20 0

5 10 15 20

Dao dong bao toan

Ep(t) Ek(t) Et(t)

0 2 4 6 8 10 12 14 16 18 20 0

5 10 15 20

Dao dong tat dan

Ep(t) Ek(t) Et(t)

-4 -3 -2 -1 0 1 2 3 4

0 0.5 1 1.5 2

Dao dong tat dan

Định dạng
Số trang	50
Dung lượng	910 KB