Have the schematic:
Solving using MathCAD:
There is an error in my equations with nodal analysis but I can't find where? May anyone help me?
I also add the solution using approach of series RLC circuit:
But it seems to be A1 and A2 constant sign is incorrect comparing my result with that in textbook.
I also tried to solve with Laplace but using Mesh Current Method, my equations are (I1 – left mesh current, I2 – right):
But same thing – I can't get properly result, may be something wrong but I can't understand what!
Best Answer
Thevenin Equiv circuit for v1 goes from 60V to 40% or 24V with Rs=30//20=12 ohms. The steady state v(t) across cap is then +24-30= -6Vdc
Then we know resonance ω= √(L/C)= v(0.5) = 0.707 and Q=XL/R = 2 π 0.5/12 which is <1 and thus overdamped and the initial voltage across cap will be 0V.
Does this method make it easier than Laplace?