Study of oscillations and how to solve in MATLAB

The oscillation of any body due to elastic force can be described by the differential equation:

y''+b*y'+(w0^2)*y =F*cos(w*t)

In which, y is oscillation displacement, b is damped coefficient, w0 is angular frequency of free oscillation, w is angular frequency of stimulating force.

This project requires students to use Matlab to solve above equation to study harmonic oscillation (no damped, no stimulated force: b = F = 0), damped oscillation (b not equal 0, F = 0), stimulated oscilation (b not equal 0, F not equal 0).

Task

- Examine the command dsolve to solve differential equation in MATLAB symbolic calculation.

- Write Matlab program to solve and plot the graph depending on time (with initial conditions y(0) = 5; y’(0) = 0):

a) harmonic oscillation (w0 = 3; b = F = 0; t = 20s)

b) damped oscillation (w0 = 10; b = 0.01, 0.1, 1.0, 10.0 ; F = 0; t = 20s) % many values of b

c) stimulated oscilation (w0 = 10; b = 0.1 ; F = 10; w= 10.0, 5.0, 3.0, 0.0; t = 150s ) % many values of w

- Discuss about the obtained results.

Please somebody can help me deal with this problem, and explain me why we have this solution, I am a newbie and trying to improve my skill day by day.Thank you.