A spring-mass system with a hardening spring (Problem 32 of Section 3.7) is acted on by a periodic external force. In the absence of damping, suppose that the displacement of the mass satisfies the initial value problem u +u+ \u u(0) = 0, u'(0) = 0. (a) Let = 1 and plot a computer-generated solution of the given problem. Does the system exhibit a beat? = COS ct, (b) Plot the solution for several values of a between 1/2 and 2. Describe how the solution changes as increases.