Chapter 4.6, Problem 16P

Consider a vibrating system described by the initial value problem

$y"+0.25y\text{'}+2y=2\cos wt$,

$y\left(0\right)=0$, $y\text{'}\left(0\right)=2$

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

(b) Find the gain function $\left|G\left(iw\right)\right|$ of the system.

(c) Plot $\left|G\left(iw\right)\right|$ and $\varphi \left(w\right)=-\arg \left(G\left(iw\right)\right)$ versus $w$.

(d) Find the maximum value of $\left|G\left(iw\right)\right|$ and the frequency $w$ for which it occurs.