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Calculate the complete response in the time domain for the second order circuit shown in Fig.5. Given

`Vs(t)=-8+2u(t)V`

. a) What are the initial values for the inductor current

`i_(L)(t)`

and capacitor voltage

`v_(c)(t)`

at the time

`t=0^(+)`

? Give brief explanations. b) Find the equation for the capacitor voltage

`v_(c)(t)`

in Fig. 5 for

`t>=0`

and show that it can be rearranged into:

`(d^(2)v_(c)(t))/(dt^(2))+(13.33)(dv_(c)(t))/(dt)+ (33333) v_(c)(t)=33333v_(s)`

You may use the direct method or the s operator method. c) Calculate the natural frequencies. What type of natural response is expected? d) Calculate the forced response. e) Use the initial conditions to calculate the complete response for

`v_(c)(t)`

for

`t>=0`

. Write the numerical representation with all numbers in decimals. Include all the units.