This problem considers responses of different second$-$order circuits, each one of three forms Form $1$: Ae$$t$/$$1+$ Be$$t$/$$2+$ C Form $2$: Ate$$t$/$$1+$ Be$$t$/$$2+$ C Form $3$: Ae$$t$/$$1$ cos$($t$)+$ Be$$t$/$$2$ sin$($t$)+$ C for time t $>0$ where $($i$)$ real$-$valued parameters A$,$ B and C denote arbitrary coefficients; $($ii$)$ positive$-$realvalued parameters $1$ and $2$ denote exponential time constants; and $($iii$)$ positive$-$real$-$valued parameter denotes a sinusoidal radian frequency. In each part below, determine the response form and specify numerical values for all relevant parameters. $($a$)$ In the below$-$left circuit, consider the inductor current i$($t$)$ given that steady$-$state conditions exist just before the switch opens. Answer: Form $1,$ A $=15/4,$ B $=15/4,$ C $=0,$ $1=1$ and $2=1/25($b$)$ In the below$-$right circuit, consider the capacitor voltage v$($t$)$ given that steady$-$state conditions exist just before the switch closes. Answer: Form $3,$ A $=2,$ B $=3/2,$ C $=0,$ $1=1/3,$ $2=1/3$ and $=4$