2. The damped vibrating system (m = 1 kg, e= 30 kg/s, k = 200 N/m) shown in the figure is initially at rest. It is then subjected to an impulse of 10 N produced by a hammer at t= Is. The governing differential equation of the problem is mz" + er + kr = r(t) where r(t) is the impulse function defined by r(t) = 10 6(t 1) For the initial conditions z(0) = 0 nnd a'(0) = 0, plot the displacement time graph of the system between 0 to 3 s.