For the network of given figure:
a. Write the mathematical expression for the current iL and the voltage vL following the closing of the switch.
b. Determine the mathematical expressions for iL and vL if the switch is opened after a period of five time constants has passed.
c. Sketch the waveforms of iL and vL for the time periods defined by parts (a) and (b).
d. Sketch the waveform for the voltage across R2 for the same period of time encompassed by iL and vL. Take careful note of the defined polarities and directions of given figure.