Editing Harmonic oscillator (section)

==Equivalent systems==
{{main|System equivalence}}
Harmonic oscillators occurring in a number of areas of engineering are equivalent in the sense that their mathematical models are identical (see [[#Universal oscillator equation|universal oscillator equation]] above).  Below is a table showing analogous quantities in four harmonic oscillator systems in mechanics and electronics.  If analogous parameters on the same line in the table are given numerically equal values, the behavior of the oscillators{{snd}}their output waveform, resonant frequency, damping factor, etc.{{snd}}are the same.

{|class="wikitable"
! Translational mechanical
! Rotational mechanical
![[RLC circuit#Series circuit|Series RLC circuit]]
![[RLC circuit#Parallel circuit|Parallel RLC circuit]]
|-
| Position <math>x</math>
| Angle <math>\theta</math>
| [[Charge (physics)|Charge]] <math>q</math>
| [[Flux linkage]] <math>\varphi</math>
|-
| [[Velocity]] <math>\frac{\mathrm{d}x}{\mathrm{d}t}</math>
| [[Angular velocity]] <math>\frac{\mathrm{d}\theta}{\mathrm{d}t}</math>
| [[Electric current|Current]] <math>\frac{\mathrm{d}q}{\mathrm{d}t}</math>
| [[Voltage]] <math>\frac{\mathrm{d}\varphi}{\mathrm{d}t}</math>
|-
| [[Mass]] <math>m</math>
| [[Moment of inertia]] <math>I</math>
| [[Inductance]] <math>L</math>
| [[Capacitance]] <math>C</math> 
|-
|[[Momentum]] <math>p</math>
|[[Angular momentum]] <math>L</math>
|[[Flux linkage]] <math>\varphi</math>
|[[Electric charge|Charge]] <math>q</math>
|-
| [[Hooke's law|Spring constant]] <math>k</math>
| [[Torsion spring#Torsion coefficient|Torsion constant]] <math>\mu</math>
| [[Elastance]] <math>1/C</math>
| [[Magnetic reluctance]] <math>1/L</math>
|-
| [[Damping ratio|Damping]] <math>c</math>
| [[Torsion spring#Motion of torsion balances and pendulums|Rotational friction]] <math>\Gamma</math>
| [[Electrical resistance|Resistance]] <math>R</math>
| [[Electrical conductance|Conductance]] <math>G = 1/R</math> 
|-
| Drive [[force]] <math>F(t)</math>
| Drive [[torque]] <math>\tau(t)</math>
| [[Voltage]] <math>v</math>
| [[Electric current|Current]] <math>i</math> 
|-
|colspan="4" align="center"| Undamped [[Resonance|resonant frequency]] <math>f_n</math>:
|-
| <math>\frac{1}{2\pi}\sqrt{\frac{k}{m}}</math>
| <math>\frac{1}{2\pi}\sqrt{\frac{\mu}{I}}</math>
| <math>\frac{1}{2\pi}\sqrt{\frac{1}{LC}}</math>
| <math>\frac{1}{2\pi}\sqrt{\frac{1}{LC}}</math>
|-
|colspan="4" align="center"| [[Damping ratio]] <math>\zeta</math>:
|-
| <math>\frac{c}{2}\sqrt{\frac{1}{km}}</math>
| <math>\frac{\Gamma}{2}\sqrt{\frac{1}{I\mu}}</math>
| <math>\frac{R}{2}\sqrt{\frac{C}{L}}</math>
| <math>\frac{G}{2}\sqrt{\frac{L}{C}}</math>
|-
|colspan="4" align="center"| Differential equation:
|-
| <math>m \ddot x + c \dot x + kx = F</math>
| <math>I \ddot\theta + \Gamma \dot\theta + \mu\theta = \tau</math>
| <math>L \ddot q + R \dot q + q/C = v</math>
| <math>C \ddot\varphi + G \dot\varphi + \varphi/L = i</math>
|}