How do I go about solving this and finding the value of v(t)?
Have you not get any notes from your teacher? What type of circuit analysis are you using?

Assuming your using complex numbers, one easy way is to first convert your circuit to phasor or frequency domain by finding the reactance's of the inductor and capacitor (jXL &amp; JXC). Then find the total circuit impedance to the voltage source by adding the real component of the resistors (be careful with resistances and reactance's in parallel).

Then use ohms law to find the total circuit current that flows. Once you know the current there are numerous different methods you could use and should be straight forward.

But with this forum you must upload some attempted solutions for people to see your level and offer help.