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.