2nd order initial value problem in matlab

[epic325]

Homework Statement

1.)I want to write a function in MATLAB that contains the 2nd order function:

20*d$^{2}$x;(dt$^{2}$)+5*dx/dt + 20*x=0 (dampened spring)

-The function should have 2 inputs (time,[initial values]) initial values should be a vector of 2 values
-The function should output a vector of the time derivatives

2.)I want to write a script that that uses the function to plot the function using euler's method with a for loop.

Homework Equations

I solved for the time derivatives

[w(2) ; -.25w(2)-w(1)] where my initial values are [1; 0] x(0)=1 and dx/dt(0)=0

The Attempt at a Solution

I think I have figured the code out but it's not plotting the right thing. it should be a dampened oscillator, but its plotting a line. I just need some help with the debugging. I will paste the function code followed by the separate script:

%This is the function where the input will be t and wVec=[initial values]

function wDerVec = odeFunc(t,wVec)
wDerVec=[wVec(2) -.25*wVec(2)-wVec(1)];
end

clear
clc
h=0.1; %h is the time step (.1s)
t=0:h:15; %time interval (0 to 15 s)
wVec=[1 0]; %initial condition

for i=2:length(t),
odeFunc(t,wVec);
wVec(i,:)=wVec(i-1,:)+ans*h;
end

plot(t,wVec(:,1)); %plots the distance with respect to time
title('Euler Approximation, damped spring');
xlabel('Time');
ylabel('distance, x');


I'm not very good at MATLAB so any help would be greatly appreciated! Thanks!

 

[jfgobin]

Good Afternoon epic325,

I tried your equation in Octave and had no problem. Here is the sequence of commands I used.

function Y=odeFCT(x,t)
Y=zeros(2,1);
Y(1)=x(2);
Y(2)=(-1/20)*(5*x(2)+20*x(1));
endfunction
t=linspace(0,50,1001);
y=lsode(@odeFCT,[1 0]',t);
plot(t,y(:,1))

Here is the graph obtained (plotted with gnuplot instead of Octave.)

Let me dive into your code.

 

[jfgobin]

Quick question -

In your code, you have

for i=2:length(t),
odeFunc(t,wVec);
wVec(i,:)=wVec(i-1,:)+ans*h;
end

Shouldn't it be

for i=2:length(t),
odeFunc(t,wVec(i-1,:));
wVec(i,:)=wVec(i-1,:)+ans*h;
end

?

 

[epic325]

Yes, jfgobin. That was the problem. Thank you very much for your help!

 

[rezeew]

As a scientist, my first suggestion would be to double check your code and ensure that all the syntax and mathematical equations are correct. It's also important to make sure that the function odeFunc is being called correctly within the for loop. Additionally, you may want to try using a smaller time step (h) to see if that improves the accuracy of your plot. Another helpful tip would be to plot the derivative values (wVec(:,2)) to see if they are changing as expected. This can help identify any errors in the calculation of the derivatives. Finally, it may be helpful to consult with a colleague or seek assistance from a tutor or online forum for further troubleshooting. Good luck with your assignment!