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Transient analysis with Laplace and nodal analysis error
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?
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 +2430= 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?

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 +2430= 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?
20180111 23:49:48