Consider the circuit above.

a$.$ Please determine IL$1($t$)$ for $t>1$ s analytically. Assume that the circuit is in steady$-$state at the time the switch changes state at $1$ s $.$

b$.$ Plot IL$1($t$)$ for $0t0\mathrm{.}1ms$ in Matlab in steps of $1$ us using the analytical equations from part a$.$ Please note that this is for the time period after the switch has changed states in the circuit. Assume that the circuit is in steady$-$state at the time the switch changes state.

c$.$ Use Circuitlab to determine IL$1($t$)$ for $999\mathrm{.}9mst1000\mathrm{.}1ms$ in steps of $1$ us $.$ Assume that the circuit is in steady$-$state at the time the switch changes state at $1$ s $.$ Note that the switch time can be defined by double$-$clicking on the switch in the circuit.