Chapter 3.8, Problem 8P

(a)

To determine

To solve: The differential equation $u^{″}+10u^{\prime }+98u=2\sin \left(\frac{t}{2}\right)$ with initial conditions $u\left(0\right)=0$ and $u^{\prime }\left(0\right)=0.03$.

(b)

To determine

The transient and steady state parts of the solution of differential equation $u^{″}+10u^{\prime }+98u=2\sin \left(\frac{t}{2}\right)$ with initial conditions $u\left(0\right)=0$ and $u^{\prime }\left(0\right)=0.03$.

(c)

To determine

To sketch: The graph of steady state solution.

(d)

To determine

The value of $\omega$ for which the amplitude of the forced response is maximum.