Hi,

how do i solve for Vs(t) for the above circuit using S-Domain analysis.

What i have done so far.
i converted the diagram into S-domain. and using source transformation, i make the current source into a voltage source ,series with the capacitor.

I did a KVL for both loops to solve for the i(s) at the capacitor (1/S). afterwards i get the Vc(S) of the capacitor as there is no current going through the resistor when t=0. so Vs(t) should be the voltage across the capacitor.

however, im stuck at the follow equation when doing inverse lap transform.
Vc(S) = 10/(s^3+3s^2+s)

how do i go about to convert it into time domain?

thanks

 

here are my workings.

 

Anyone could Advice ?

 

Vc(S) = 10/(s^3+3s^2+s) do a partial fraction decomposition and then use that to do an inverse laplace to find your time domain response

 

Vc(S) = 10/(s^3+3s^2+s) do a partial fraction decomposition and then use that to do an inverse laplace to find your time domain response

how to do a partial fraction on that equation?
what i get is
A/S + Bs+c/(s^2+3s+1) .
but for my demoniantor (s^2+3s+1), it cannot be factorize out