Chapter 8.5, Problem 55AYU

Charging a Capacitor See the illustration. If a charged capacitor is connected to a coil by closing a switch, energy is transferred to the coil and then back to the capacitor in an oscillatory motion. The voltage $V$ (in volts) across the capacitor will gradually diminish to 0 with time $t$ (in seconds).

(a) Graph the function relating $V\text{ and }t$:

$V\left(t\right)=e^{-t/3}\cos \left(\pi t\right)\text{ 0 }\le t\le \text{ 3}$

(b) At what times $t$ will the graph of $V$ touch the graph of $y=e^{-t/3}$? When does the graph of $V$ touch the graph of $y=-e^{-t/3}$?

(c) When will the voltage $V$ be between $-0.4\text{ and }0.4$ volt?