Switch in the Circuit Shown Below Has Been Opened for a Long

Essay

switch in the circuit shown below has been opened for a long time before it is closed at t $= 0$ . Find the voltage $\mathrm { v } ( \mathrm { t } )$ across the capacitor for $\mathrm { t } \geq 0$ . Assume $\mathrm { R } _ { 1 } = 500 \Omega , \mathrm { R } _ { 2 } = 1 \mathrm { k } \Omega , \mathrm { L } = 200$ $\mathrm { mH } , \mathrm { C } = 0.05 \mu \mathrm { F } , \mathrm { V } _ { \mathrm { s } } = 3 \mathrm {~V} , \mathrm { i } ( 0 ) = \mathrm { I } _ { 0 } = 1 \mathrm {~mA} , \mathrm { v } ( 0 ) = \mathrm { V } _ { 0 } = 0.5 \mathrm {~V}$