Plot a second order equation and plot two equations on the same grafic

Hi everyone,

1. I can't plot this function in a grafic, I think the code in the editor is not right. The second order equation is:

(a) dx^2/dt^2 (t) = -xg0*w0^2*sin(wf*t)-w0^2*x-2*M*w0*beta*dx/dt

xg0, w0, M, beta are constants.

2. Plot two solutions in the same grafic.

I already solve other system with ode45, now i want to plot that second order equation with one solution of this sistem.

It is a enginneering problem that consist in a structure with and without a vibration control system. One equation (a) give me the response without that control and the system of equations give me the response with that control... I need to compare that in the same grafic.

Thank's everyone.

Answer 1

[Kevin Holst]

You can plot multiple sets of data on one figure multiple ways. The first way would be:

plot(x1,y1,x2,y2,...)

The next most common would involve using hold:

plot(x1,y1)
hold on
plot(x2,y2)

[Igor]

Yes that work but in my case I can't do it like that. Because:

EDITOR:

1. Equation: It is my first problem because I can define in EDITOR the second order equation that I descrive on the first coment

2. Equation system:

s=@(t,y) [y(3); y(4); (-(M+mv*A*L)*xg0*w0^2*sin(wf*t)-M*w0^2*y(1)-2*M*w0*beta*y(3)-mv*A*alfa*L*((mv*A*alfa*L*((M+mv*A*L)*xg0*w0^2*sin(wf*t)+M*w0^2*y(1)+2*M*w0*beta*y(3))+(M+mv*A*L)*(-mv*A*alfa*L*xg0*w0^2*sin(wf*t)-2*mv*A*g*y(2)-(1/2)*mv*A*delta*abs(y(4))*y(4)))/(mv*A*L*(M+mv*A*L)-(mv*A*L)^2)))/(M+mv*A*L);(mv*A*alfa*L*((M+mv*A*L)*xg0*w0^2*sin(wf*t)+M*w0^2*y(1)+2*M*w0*beta*y(3))+(M+mv*A*L)*(-mv*A*alfa*L*xg0*w0^2*sin(wf*t)-2*mv*A*g*y(2)-(1/2)*mv*A*delta*abs(y(4))*y(4)))/(mv*A*L*(M+mv*A*L)-(mv*A*L)^2)];

[T,Y]= ode45(s,[0 30],[0 0 0 0]);

To plot just the solution of the system I use plot(T,Y(:,1)) (for example). But I want to plot this solution 1 and the second order equation, on the same plot.

Can you help me ?

[Kevin Holst]

So you're wanting to plot s and Y on the same plot? If so, what will s be a function of, t?

fplot is probably what you want to use to get s plotted, however, it only works for functions with one variable. If you can treat y as a constant in your s function for the purposes of this plot I'd suggest doing so. Maybe:

s_ = @(t) s(t,y);

fplot(s_,[0 30])

[Igor]

I can plot all the solutions off the system s, funtion of time (t) with the comand plot(T,Y(:,1)) (for example). What I can't do is define the equation:

dx^2/dt^2 (t) = -xg0*w0^2*sin(wf*t)-w0^2*x-2*M*w0*beta*dx/dt

on the EDITOR and than plot it. After define that funtion, in the end I want to plot the two functions in the same grafic.

I send you my EDITOR:

M=0.577;

mv=1000;

A=1.157*10^-5;

xg0=0.05;

w0=5.17;

wf=5.3;

beta=2/100;

alfa=0.7;

L=0.734;

g=9.81;

delta=0.5;

%Define Equation1 -I CAN'T DEFINE THIS

dx^2/dt^2 (t) = -xg0*w0^2*sin(wf*t)-w0^2*x-2*M*w0*beta*dx/dt ???

%Define System - OK!

s=@(t,y) [y(3); y(4); (-(M+mv*A*L)*xg0*w0^2*sin(wf*t)-M*w0^2*y(1)-2*M*w0*beta*y(3)-mv*A*alfa*L*((mv*A*alfa*L*((M+mv*A*L)*xg0*w0^2*sin(wf*t)+M*w0^2*y(1)+2*M*w0*beta*y(3))+(M+mv*A*L)*(-mv*A*alfa*L*xg0*w0^2*sin(wf*t)-2*mv*A*g*y(2)-(1/2)*mv*A*delta*abs(y(4))*y(4)))/(mv*A*L*(M+mv*A*L)-(mv*A*L)^2)))/(M+mv*A*L);(mv*A*alfa*L*((M+mv*A*L)*xg0*w0^2*sin(wf*t)+M*w0^2*y(1)+2*M*w0*beta*y(3))+(M+mv*A*L)*(-mv*A*alfa*L*xg0*w0^2*sin(wf*t)-2*mv*A*g*y(2)-(1/2)*mv*A*delta*abs(y(4))*y(4)))/(mv*A*L*(M+mv*A*L)-(mv*A*L)^2)];

[T,Y]= ode45(s,[0 30],[0 0 0 0]);

%PLOT TWO SOLUTIONS - I CAN'T DO THIS

plot (T,Y(:,1), dx^2/dt^2 (t)) ?????

[Igor]

I just can define that first equation with:

r=@(t,y) [y(3); y(4); -xg0*w0^2*sin(wf*t)-w0^2*y(1)-2*M*w0*beta*y(3); 0];

[T,Y]= ode45(r,[0 30],[0 0 0 0]);

Even this way I can plot r and s in the same grafic.. Some help?

[Kevin Holst]

If y is a vector that's constant, I would leave it out of the inputs for the equations that you want to plot. If it's in the workspace, it will be picked up. So your dx^2/dt^2(t) and s equations could probably be written like this for plotting purposes:

dx2dy2_plot = @(t) -xg0*w0^2*sin(wf*t)-w0^2*x-2*M*w0*beta*y(3);

s_plot = @(t) (-(M+mv*A*L)*xg0*w0^2*sin(wf*t)-M*w0^2*y(1)-2*M*w0*beta*y(3)-mv*A*alfa*L*((mv*A*alfa*L*((M+mv*A*L)*xg0*w0^2*sin(wf*t)+M*w0^2*y(1)+2*M*w0*beta*y(3))+(M+mv*A*L)*(-mv*A*alfa*L*xg0*w0^2*sin(wf*t)-2*mv*A*g*y(2)-(1/2)*mv*A*delta*abs(y(4))*y(4)))/(mv*A*L*(M+mv*A*L)-(mv*A*L)^2)))/(M+mv*A*L);(mv*A*alfa*L*((M+mv*A*L)*xg0*w0^2*sin(wf*t)+M*w0^2*y(1)+2*M*w0*beta*y(3))+(M+mv*A*L)*(-mv*A*alfa*L*xg0*w0^2*sin(wf*t)-2*mv*A*g*y(2)-(1/2)*mv*A*delta*abs(y(4))*y(4)))/(mv*A*L*(M+mv*A*L)-(mv*A*L)^2)

then you can just execute the following plot command

figure

hold on

fplot(s_plot,[0 30])

fplot(dy2dx2_plot,[0 30])

[Igor]

It doesn't work =\. I think I explain something not right.

1. System of equation

s=@(t,y) [y(3); y(4); (-(M+mv*A*L)*xg0*w0^2*sin(wf*t)-M*w0^2*y(1)-2*M*w0*beta*y(3)-mv*A*alfa*L*((mv*A*alfa*L*((M+mv*A*L)*xg0*w0^2*sin(wf*t)+M*w0^2*y(1)+2*M*w0*beta*y(3))+(M+mv*A*L)*(-mv*A*alfa*L*xg0*w0^2*sin(wf*t)-2*mv*A*g*y(2)-(1/2)*mv*A*delta*abs(y(4))*y(4)))/(mv*A*L*(M+mv*A*L)-(mv*A*L)^2)))/(M+mv*A*L);(mv*A*alfa*L*((M+mv*A*L)*xg0*w0^2*sin(wf*t)+M*w0^2*y(1)+2*M*w0*beta*y(3))+(M+mv*A*L)*(-mv*A*alfa*L*xg0*w0^2*sin(wf*t)-2*mv*A*g*y(2)-(1/2)*mv*A*delta*abs(y(4))*y(4)))/(mv*A*L*(M+mv*A*L)-(mv*A*L)^2)];

[T,Y]= ode45(s,[0 30],[0 0 0 0]);

- This is ok, I can plot the 4 solutions of the system with plot(T,Y(:,1)), solution 1 for example.

2. I define that second order equation and solve with ode45

r=@(t,y) [y(3); y(4); -xg0*w0^2*sin(wf*t)-w0^2*y(1)-2*w0*beta*y(3); 0];

[T,Y]= ode45(r,[0 30],[0 0 0 0]);

3. If the 2. is right, now I want to plot two solution on the same grafic. Isolate I can plot with the command plot(T,Y(:,1)).. But I don't now the command to plot the two. Already try:

plot(T,Y1(:,1),T,Y2(:,1)) , and other things that doesn't work.

I really appreciate the help you given to me, really ;)

[Kevin Holst]

try

[Ts,Ys]= ode45(s,[0 30],[0 0 0 0]);

[Tr,Yr]= ode45(r,[0 30],[0 0 0 0]);

plot(Ts,Ys(:,1),Tr,Yr(:,1))

[Igor]

Worked, finally...thank's to you. Thank you very much.

Just a final question, make sense define and calculate the equation:

dx^2/dt^2 (t) = -xg0*w0^2*sin(wf*t) - w0^2*x - 2*M*w0*beta*dx/dt

with:

r=@(t,y) [y(3); y(4); -xg0*w0^2*sin(wf*t)-w0^2*y(1)-2*w0*beta*y(3); 0];

[T,Y]= ode45(r,[0 30],[0 0 0 0]);

- I say this because it is a system of 4 equations to solve just one. don't now if that make sense.

Tank's.

[Kevin Holst]

Hmm... I don't have too much experience with using ode45, but it looks like you could just solve:

r = @(t) -xg0*w0^2*sin(wf*t)-w0^2*y(1)-2*w0*beta*y(3);

[T,Y] = ode45(r,[0 30],0);

It looks like ode45 solves each equation independently, but I might be wrong about that.

[Kevin Holst]

Also, don't forget to click accept answer under my name up there.

[Igor]

I have some other problem with my dissertation, sorry stop answering. I am a finalist of civil engineering.

All you say it works, thank's to you I have the program correct. Thank you.

I have another question. Now I have two functions in the same graphic. I need to calculate each maximum to calculate the effectiveness of the control system. What is the code for each function?

I send to a reduce EDITOR:

M=0.577;

mv=1000;

A=1.157*10^-5;

xg0=0.05;

w0=5.17;

wf=5.17;

beta=2/100;

alfa=0.7;

L=0.734;

g=9.81;

delta=0.5;

%Equation 1

r=@(t,y) [y(3); y(4); -xg0*w0^2*sin(wf*t)-w0^2*y(1)-2*w0*beta*y(3); 0];

[Tr,Yr]= ode45(r,[0 50],[0 0 0 0]);

%System of equations

s=@(t,y) [y(3); y(4); (-(M+mv*A*L)*xg0*w0^2*sin(wf*t)-M*w0^2*y(1)-2*M*w0*beta*y(3)-mv*A*alfa*L*((mv*A*alfa*L*((M+mv*A*L)*xg0*w0^2*sin(wf*t)+M*w0^2*y(1)+2*M*w0*beta*y(3))+(M+mv*A*L)*(-mv*A*alfa*L*xg0*w0^2*sin(wf*t)-2*mv*A*g*y(2)-(1/2)*mv*A*delta*abs(y(4))*y(4)))/(mv*A*L*(M+mv*A*L)-(mv*A*L)^2)))/(M+mv*A*L);(mv*A*alfa*L*((M+mv*A*L)*xg0*w0^2*sin(wf*t)+M*w0^2*y(1)+2*M*w0*beta*y(3))+(M+mv*A*L)*(-mv*A*alfa*L*xg0*w0^2*sin(wf*t)-2*mv*A*g*y(2)-(1/2)*mv*A*delta*abs(y(4))*y(4)))/(mv*A*L*(M+mv*A*L)-(mv*A*L)^2)];

[Ts,Ys]= ode45(s,[0 50],[0 0 0 0]);

%Graphic

plot(Ts,Ys(:,1),Tr,Yr(:,1))

% Effectiveness of the system ????

Tank's.