Get results of output for each one value of the input - MATLAB ODE

Question

I am simulating a mass - damper - system in Matlab and I have the following vector (1x100) as input to my system:

ut = linspace(0, 10);
u = 5 * sin(2 * ut) + 10.5; % input of our system - external force

Now, I want to take the value of the output for each value of the input vector using this differential equation:

function dx = odefun_4(t,x)
    m = 15;
    b = 0.2;
    k = 2;   
    dx = [x(2); u/m - (b/m)*x(2) - (k/m)*x(1)];    
end

which is called from my main .m file like this:

[t,X] = ode45(@odefun_4, [0 10], [0;0])

I tried to pass the u vector by making it global variable but I get an error stating: Dimensions of arrays being concatenated not consistent. I also tried to set the Refine parameter using odeset and the options argument of ode45 solver but still don't get the desired results. I could really use some help.

Answer 1

If you want $u$ to be considered as a smooth continuous function, then you should define it as such since you also have $t$ available as well. So you could use:

function dx = odefun_4(t,x)
    m = 15;
    b = 0.2;
    k = 2;
    u = 5 * sin(2 * t) + 10.5;
    dx = [x(2); u/m - (b/m)*x(2) - (k/m)*x(1)];
end

I often also find it more convenient to use anonymous functions in Matlab, for example:

m = 15;
b = 0.2;
k = 2;
u = @(t) 5 * sin(2 * t) + 10.5;
odefun_4 = @(t,x) [x(2); u(t)/m - (b/m)*x(2) - (k/m)*x(1)];