Compare $LC$ oscillations and forced damped oscillations in mechanics.

(N/A) The equation of motion for a forced damped mechanical oscillator is given by:
$m \frac{d^{2} x}{d t^{2}} + b \frac{d x}{d t} + k x = F_{0} \cos \omega_{d} t$
The equation for a driven $LCR$ circuit is given by:
$L \frac{d^{2} q}{d t^{2}} + R \frac{d q}{d t} + \frac{q}{C} = V_{m} \sin \omega t$
By comparing these two differential equations, we can establish an analogy between mechanical and electrical systems as follows:

Mechanical System (Forced Oscillations)	Electrical System (Driven $LCR$ Circuit)
Displacement $x$	Charge $q$
Mass $m$	Inductance $L$
Damping constant $b$	Resistance $R$
Spring constant $k$	Inverse capacitance $1/C$
Driving force $F_{0} \cos \omega_{d} t$	Driving voltage $V_{m} \sin \omega t$
Natural frequency $\omega_{0} = \sqrt{k/m}$	Natural frequency $\omega_{0} = 1/\sqrt{LC}$