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# (Solved): Calculate the complete response in the time domain for the second order circuit shown in Fig.5. Gi ...

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.

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