Compare the oscillations in an $LC$ circuit with the oscillations of a block attached to a spring.

(N/A) The $LC$ oscillation is analogous to the mechanical oscillation of a block attached to a spring.
The differential equation for $LC$ oscillation is $\frac{d^{2} q}{d t^{2}} + \frac{q}{LC} = 0$, which can be written as $\frac{d^{2} q}{d t^{2}} + \omega_{0}^{2} q = 0$.
For a block of mass $m$ oscillating with frequency $\omega_{0}$, the equation is $\frac{d^{2} x}{d t^{2}} + \omega_{0}^{2} x = 0$, where $\omega_{0} = \sqrt{\frac{k}{m}}$ and $k$ is the spring constant.
In mechanics, $k = \frac{F}{x}$, representing the force required to produce unit extension or compression. Its unit is $N \cdot m^{-1}$.
In an $LC$ circuit, the corresponding equation is $V = \frac{q}{C}$, so $\frac{1}{C} = \frac{V}{q}$, representing the potential difference required to store unit charge.
The following table shows the analogies between mechanical and electrical quantities:

Mechanical system	Electrical system
Mass $m$	Inductance $L$
Force constant $k$	Reciprocal capacitance $1/C$
Displacement $x$	Charge $q$
Velocity $v = \frac{dx}{dt}$	Current $I = \frac{dq}{dt}$
Mechanical energy $E = \frac{1}{2} k x^{2} + \frac{1}{2} m v^{2}$	Electromagnetic energy $E = \frac{1}{2} \frac{q^{2}}{C} + \frac{1}{2} L I^{2}$