Consider a vibrating system described by the initial value problem.

u'' + 1/4 u' + 2u = 2cos(wt), u(0) = 0. u'(0)= 3.

(a) determine the steady state part of the solution of this problem.

(b) find the amplitude a of the steady state solution in terms of ? .

(c) find the maximum value of a and the frequency ? for which it occurs.