5. Put your Calculus I skills to use to answer the following optimization problems.

(a) For the underdamped mass-spring system with m = 1, b = 2, k = 3 and a(0) = 1, ż(0) = 0, find the maximum displace-

ment attained for t > 0.

* (0) = 2, find the maximum

(b) For the critically damped mass-spring system with m = 1, b = 4, k = 4 and x(0)

displacement attained for t > 0.