Given the electrical system below. The output is the voltage across the capacitor.

a$.$ Determine the mathematical model of the system in differential equation

b$.$ Determine the transfer function of the system

c$.$ Compute manually the unit step response of the system

d$.$ What is the steady state error of the unit step response? Express the steady state error in term of Kp $($the steady state error constant for unit step response$)$ and compute the value of Kp

e$.$ Make a computer simulation to simulate the unit step response of the system, and show that your solution in point $($c$)$ and $($d$)$ are correct.