I'd like to draw a graph of mechanical vibration with a matlap....

[Dyuman Joshi]

The question says "All of your codes constructed by your own algorithm".

So, what have you tried yet?

[John D'Errico]

Homework is assigned to you, so that you will learn by doing. If you do nothing, then why should we do your work and thinking for you?

Answer 1

[Sam Chak]

Hi @Hac Li

Your teacher won't approve this code as it utilizes the MATLAB built-in ODE solver. However, you can compare the results with your own algorithm. By 'own algorithm,' I mean that you may need to devise a new solver algorithm. You can take inspiration from Dr. Alan C. Hindmarsh, who developed several ODE packages. He is the creator of the Livermore Solver for Ordinary Differential Equations, known as LSODE().

% MATLAB built-in ODE solver
F              = ode;
F.Parameters   = 10;
F.InitialValue = [1; 0];
F.ODEFcn       = @(t, y, p) [      y(2); 
                             - 0.5*y(2) - 200*y(1) + 1*cos(2*pi/p*t)];
F.Solver       = "ode78";
S              = solve(F, 0, 30);

% Plotting the graph
plot(S.Time, S.Solution(1,:)), grid on
xlabel('Time')

Answer 2

[Sulaymon Eshkabilov]

An initial step will be looking at the Runge-Kutta method Runge-Kutta and its implementation in MATLAB - writing a code like THIS ONE.