(Solved): The switch in the circuit shown in Figure. has been in position \( a \) for a long time before it ...

The switch in the circuit shown in Figure. has been in position \( a \) for a long time before it is moved to position \( b \) at time \( t=0 \). a. Find the current through the inductor \( I_{0} \) (from left to right) and the voltage across the capacitor \( V_{0} \) (from top to bottom) at \( t=0 \). b. Write a mesh equation on the left side of the circuit for \( t \geq 0 \). c. Write a node equation on top of the capacitor for \( t \geq 0 \). d. Find the second-order differential equation in \( v(t) \) for \( t \geq 0 \). e. Find the voltage across the capacitor, \( v(t) \), for \( t \geq 0 \). f. Find the current through the inductor, \( i(t) \), for \( t \geq 0 \).