Use the circuit diagram below to answer the fol-lowing questions and imperatives. Let Iş = Ao,where A, >0 is a known constant. Perform a fullcircuit analysis, including the transient response.The

initial inductor current is i (0) = 0 and theinitial capacitor voltage is vc(0) = 0. Assume thedamping ratio E (0, 1); i.e. the system is under-damped and the roots of the characteristic equa-tion are complex. (a) Write the elemental, KCL, and KVL equations. (b) Write the second-order differential equation for il (t) arranged in the standard form and identify the natural frequency wn and damping ratio Č. (c) Convert the initial condition in vc to a second initial condition in i̟. (d) Solve the differential equation for iL (t) and use the solution to find the output voltage vo(t). It is acceptable to use a known solution and to express your solution in terms of wn and č.