Harmonic Oscillator Analogy

An RLC circuit has much in common with a harmonic oscillator. In fact, the various components of an RLC circuit correspond quite well with the various components of a harmonic oscillator. Here are the various correspondences. Note that the coefficients do not actually match up exactly in their respective equations, but rather that they appear in the same terms:

1. Charge $\left(Q\right)$ corresponds to position $\left(x\right)$

2. Current $\left(I = \frac{dQ}{dt}\right)$ corresponds to velocity $\left(v = \frac{dx}{dt}\right)$

3. Inductance $\left(L\right)$ corresponds to mass $\left(m\right)$: The inductor in an RLC circuit resists changes in the current, just as the mass in a harmonic oscillator resists changes in the velocity.

4. Resistance $\left(R\right)$ corresponds to the drag coefficient $\left(b\right)$: The resistor dissipates energy and resists the passage of current, just as the drag force resists the movement of the mass and dissipates its kinetic energy.

5. The driving potential $\left(V\right),$ if there is one, corresponds to the driving force $\left(F\right),$ if there is one: Both of them, if present, force an oscillation in a quantity which would otherwise decay.

6. Capacitance $\left(C\right)$ corresponds to the spring constant $\left(k\right)$: The capacitor stores energy proportional to the square of the charge, just as the spring stores energy proportional to the square of the position.