The step transient response of a parallel RLC circuit
The mechanical equivalent of an LC resonant circuit can be regarded as a physical mass suspended by a spring: -

http://www.math.umt.edu/golubtsov/412_418_PDE/Movies/FourierSeriesandBVPs/MassSpring.gif

This is well known to anybody from an early age but the oscillation type being sinusoidal doesn't become apparent until you study engineering.

The picture above does not contain any damping (equivalent to a resistor) so the oscillations continue forever. If damping is applied this happens (shown from a different angle: -



The "spring" is the green thing that ironically looks like a resistor. The red square is the "mass" running on a notionally friction-less bed and the blue rectangle is the dampener.

Formulaically the spring-mass system has a resonant frequency that is: -



k is spring stiffness and is equivalent (depending on how you regard force as an electrical analogue) to the inverse of inductance. M is equivalent to capacitance.

And for an LC circuit the formula is: -