with *y > Z and the critically damped dierential equation de dy E+2E+y=0 Each particle is initially at rest with initial displacement at t = 0 to be 1. Show that $(t) > y(t) for all t > 0. This exercice demonstrates that a critically damped mechanical system approaches equilibrium faster than an overdamped system. Hint: Let 205) = $05) y(t). Show that z is the solution of Z" + 22' + z = f(t) with zero initial conditions, where f (t) = (2 7)% > 0 for all t > 0. Use then the variation of parameters formula to show that z(t) > 0 for all t > 0. 1