If a LC circuit is considered analogous to a harmonically oscillating spring block system, which energy of the LC circuit would be analogous to potential energy and which one analogous to kinetic energy?

Question

If a LC circuit is considered analogous to a harmonically oscillating spring block system, which energy of the LC circuit would be analogous to potential energy and which one analogous to kinetic energy?

Philoid · Accepted Answer

Note that for a mass on o a spring,

where KE is the kinetic energy, PE is the potential energy, k is the spring constant, x is the position with x = 0 at equilibrium, v is the speed of the object and m is the mass.

Note that

For an LC circuit,

where U_c and U_L are the energy stored by the capacitor and inductor respectively, Q is the charge on the capacitor, C is the capacitance, L is the inductance and I is the instantaneous current through the circuit.

Note that

Because of these equations, we can see that Q is analogous to x and I is analogous to v. Thus, the energy stored by the capacitor is analogous to the potential energy, and the energy stored by the inductor is analogous to the kinetic energy.