L-C Oscillation

Consider a L-C oscillation circuit. Circuit elements has zero resistance. Initially at t=0 all the energy is stored in the form of electric field and plate-1 is having positive charge: at time t=t_(1) plate-2 attains half of the maximum=ve change for the first time. Value of t_(1) is :

A capacitor of capacitance 1 mu F is charged to a potential of 20 volt. The battery is then disconnected and a pure inductive coil of inductance 10 mH is connected across the capacitor so that L-C oscillation are set-up in the circuit. What is the maximum current in the circuit?

L R Oscillation

L R Oscillation

D is disturbed, and ultimately all the pendulums start oscillating. Match the following {:("1. Oscillations of A","(a) free oscillation"),("2. Oscillations of B","(b) forced oscillation"),("3. Oscillations of C","(c) Resosnant oscillation"),("4. Oscillations of D",):}

An inductor of inductance 2 mH is connected across a charged capacitor of capacitance 5 mu F and the L-C circuit is set oscillating at its natural frequency. What is the natural angular frequency of its oscillations?