Chapter 4.6, Problem 7P

(a) Find the solution of Problem 5.

(b) Plot the graph of the solution.

(c) If the given external force is replaced by a force $A\exp \left(i\omega t\right)$ of frequency $\omega$, find the frequency response $G\left(i\omega \right)$, the gain $\left|G\left(i\omega \right)\right|$, and the phase $\varphi \left(\omega \right)=-\arg \left(G\left(i\omega \right)\right)$. Then find the value of $\omega$ for which resonance occurs.

5. A mass weighing $4$ pounds (lb) stretches a spring $1.5\text{in}$. The mass is displaced $12\text{in}\text{.}$ in the positive direction from its equilibrium position and released with no initial velocity. Assuming that there is no damping and that the mass is acted on by an external force of $7\cos 3t$ lb, formulate the initial value problem describing the motion of the mass.