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I am trying to figure out how to find \$V_c(t)\$ for \$t \geq 0\$ in this.

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    \$\begingroup\$ First you need to work out the current in the inductor and voltage across the capacitor for t=0. Have you calculated it ? If so, please edit it into the question. \$\endgroup\$ – AJN Sep 23 '20 at 16:26
  • \$\begingroup\$ for t geq 0 - what does that mean? \$\endgroup\$ – Andy aka Sep 23 '20 at 17:07
  • \$\begingroup\$ What have you tried so far? \$\endgroup\$ – JYelton Sep 23 '20 at 17:14
  • \$\begingroup\$ @Andyaka geq is ≥ - I edited the title accordingly. \$\endgroup\$ – JYelton Sep 23 '20 at 17:15
  • \$\begingroup\$ You could try to find the Vc/Vin transfer function \$\endgroup\$ – Ben Sep 23 '20 at 19:55

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