Chapter 8.6, Problem 40P

In $(6.38),$ show that for a given forcing frequency ${\omega }^{\prime },$ the displacement $y$ and the velocity $dy/dt$ have their largest amplitude when $\omega ={\omega }^{\prime }$.

For a given $\omega$, we have shown in Section 6 that the maximum amplitude of $y$ does not correspond to ${\omega }^{\prime }=\omega .$ Show, however, that the maximum amplitude of $dy/dt$ for a given $\omega$ does correspond to ${\omega }^{\prime }=\omega$.

State the corresponding results for an electric circuit in terms of L, R, C.