(a) Use the general solutions x(t) to the differential equation d2 x/dt2 + 2dx/dt + w2/0 x = 0 for under damped, critically damped, and

(a) Use the general solutions x(t) to the differential equation d2 x/dt2 + 2βdx/dt + w2/0 x = 0 for under damped, critically damped, and over damped motion and choose the constants of integration to satisfy the initial conditions x = x0 and v = v0 = 0 at t = 0.;
(b) Use a computer to plot the results for x (t) x0 as a function of w0t in the three cases β = (1/2) w0, β = w0, and β = 2w0. Show all three curves on a single plot.