Error when using ODE45

Hello

I'm trying to write a code to solve a system of differential equations. One of the given conditions is F(0) = f(t). However when I try and implement that in the code I get an error. I believe that's because ode45 only wants variable inputs for the conditions. How do I get around this?

p_max = 50;
t     = 2;   % seconds
T     = 0.2; % seconds
tau   = 2;   % seconds
c     = 5;   % m/s
L     = 10;  % meters
h     = 5;

t = linspace(1,0.2,1000);

for i=1:1000

f(i) = (5/2)*(1-cos(2*pi*t(i)/T));

end

figure(1)
plot(t,f);

syms x y z
% t = x
% r = y
% p = z

F = @(t,x) [x(2); ((c^2)*(100/h^2)) - (1/tau)*x(2)]; 

[t,xa] = ode45(F,[0 20],[f 0]);

figure(2)
plot(t,xa(:,2))
title('y(t)')
xlabel('t'), ylabel('y')

Problem statement:

he series of the 2nd order ODE can be further reduced to a series of 1st order ODE, as shown in equation (40). The ODE system can be numerically solved with Matlab ODE45. Using the values of the parameters described in this paper, develop your matlab code to reproduce the results of Figures 2a and 2b in this paper based on the Maxwell material model.

Equation 40:

Initial Condition function:

Figures 2a and 2b:

Answer 1

[Star Strider]

What do actually want to do?

If ‘f’ is a forcing function, incorporate it with ‘t’ as an input to your differential equation, not as an initial condition.

See for example: ODE with Time-Dependent Terms (link).

[Westin Messer]

I want 'f' to be an initial condition in the ode45 but that's where I'm getting the error.

[Westin Messer]

The example you sent is a lot different because the 'f(t)' functions are in their differential equations. However in my case the 'f(t)' function is an initial condition.

[James Tursa]

Can you post the actual text of the problem statement?

[Westin Messer]

Yes, I have edited the question.