Transient analysis with Laplace and nodal analysis error
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 &lt;1 and thus overdamped and the initial voltage across cap will be 0V.

Does this method make it easier than Laplace?