The mechanical-electrical analogy

Remark — The mechanical-electrical analogy

The same mathematical object — the equation $\ddot y + 2\gamma\dot y + \omega_0^2 y = 0$ — describes very different physical systems: springs, pendulums, circuits, atomic oscillations. This is the power of mathematical language: a single equation, infinitely many realisations.

It is worth recalling the dictionary of correspondences between the mechanical world and the electrical one:

Mechanical	Electrical	Role
$m$	$L$	inertia
$\gamma$	$R$	dissipation
$k$	$1/C$	restoring
$x$	$Q$	dynamical variable

Links

Topics: Differential equations
Concepts: Second-order linear ODE · Harmonic oscillator
Skills: Modelling