Chapter D2.5, Problem 23E

a.

To determine

To explain: The reason for local maximum value of g to occur at the same points as the local minimum of denominator.

b.

To determine

To explain: The reason for local maximum value of g to occur at the same points as the local minimum of value of the $h\left(\omega \right)={\left({\omega }_0{}^2-\omega \right)}^2+b^2{\omega }^2$

c.

To determine

To show: The value of $h^{\prime }\left(\omega \right)=2\omega \left(b^2-2{\omega }_0{}^2+2{\omega }^2\right)$.

d.

To determine

To show: If $b<\sqrt{2}{\omega }_0$ then g has local maximum at $\omega =\sqrt{{\omega }_0{}^2-\frac{b^2}{2}}$

e.

To determine

To show: That the Gain function is monotonically decreasing for $\omega >0$ if $b\ge \sqrt{2}{\omega }_0$ and has local maximum $\omega =0$.

f.

To determine

To explain: Which among the following part of (d) and (e) corresponds the strong damping.