Hello I need help with solving this problem which deals with Electrical Circuit analysis. Please show all the correct st

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Hello
I need help with solving this problem which deals with Electrical Circuit analysis. Please show all the correct steps and the correct answers to each part of the question
Please follow all of the directions for each part of the question.
Also please provide the correct answer with the correct steps with each specific part of the question in complete detail.
Please provide pictures of circuits if required (very important). Please draw the circuit for this problem and make sure it's very detailed.
Please make sure that your work is correct and I promise that I will rate you.
1. For the following circuit, switch is closed at t=0. a. Write a differential equation in i(t). b. Find a and wo. c. Find the characteristic equation and the roots of the characteristic equation. d. Find the final value of current i(t) through the inductor. e. Find current i(t) through the inductor for t > 0 and sketch i(t). f. Find voltage v(t) for t≥ 0 and sketch v(t). PS Switch S Vs 20V R1 ΣΚΩ www. R2 2k52 v(t) V=4V HII. C 50 nF 35 pol i(t) L 40mH lo-5mA