A capacitor can be made physically using two parallel conducting plates which are held close together (but not touching). Electric charge can be stored in a capacitor by applying a voltage across the plates.
The defining equation of a capacitor is
where denotes the capacitor's charge in Coulombs, is the capacitance in Farads, and is the voltage drop across the capacitor in volts. Differentiating with respect to time gives
Taking the Laplace transform of both sides gives
Assuming a zero initial voltage across the capacitor at time 0, we have
Mechanical Equivalent of a Capacitor is a Spring
The mechanical analog of a capacitor is the compliance of a spring. The voltage across a capacitor corresponds to the force used to displace a spring. The charge stored in the capacitor corresponds to the displacement of the spring. Thus, Eq.(E.2) corresponds to Hooke's law for ideal springs:
Example Analog Filter