Matlab Simulink - How to simulation this math?

Answer 1

[Ameer Hamza]

You need to use ode45(): https://www.mathworks.com/help/matlab/ref/ode45.html . Convert your 2nd order ODE into a system of 2 first-order ODEs. The following code assumes F(t)=1.

tspan = [0 10];
IC = [0; 0]; % initial condition
[t, X] = ode45(@odeFun, tspan, IC);

plot(t, X, '-o')
legend({'$x$', '$\dot{x}$'}, 'FontSize', 16, 'Interpreter', 'latex', 'Location', 'best')

function dxdt = odeFun(t, x)
    c = 2;
    k = 1;
    m = 5;
    
    F = 1;
    
    dxdt = zeros(2,1);
    dxdt(1) = x(2);
    dxdt(2) = (F - c*x(2) - k*x(1))/m;
end