Find the current i$($t$)$ for t $>0$ in the circuit shown below.

a$)$ What are the roots s$1$ and s$2?$

b$)$ Is this over damped, underdamped, or critically damped?

c$)$ Write the general form of the current equation

d$)$ Find the initial conditions for i$($t$)$ and di$//$dt

e$)$ Use the initial conditions to solve for the constants in your equation.