Hello aspirant

LC circuits are used either for generating signals at a particular frequency of picking out a signal at a particular frequency from a more complex signal, this function is called banpass filter.

Time constant is the time taken ( after a switch is opened it closed) for the voltage ( or some other  variable  but usually we are interested in the voltage across a capacitor ) to reach about 63% of it's long term study state value.

The time constant in a series RC circuit is R*C. The time constant in a series RL circuit is L/R