Mechanical Equivalent of a Capacitor is a Spring

The mechanical analog of a capacitor is the compliance of a spring. The voltage $v(t)$ across a capacitor $C$ corresponds to the force $f(t)$ used to displace a spring. The charge $q(t)$ stored in the capacitor corresponds to the displacement $x(t)$ of the spring. Thus, Eq. (C.2) corresponds to Hooke's law for ideal springs:

$$x(t) = \frac{1}{k} f(t),$$

where $k$ is called the spring constant or spring stiffness. Note that Hooke's law is usually written as $f(t) = k\,x(t)$. The quantity $1/k$ is called the spring compliance.