Harmonic Oscillator - Equivalent Systems

Equivalent Systems

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 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—their output waveform, resonant frequency, damping factor, etc.—are the same.

Translational Mechanical Torsional Mechanical Series RLC Circuit Parallel RLC Circuit
Position Angle Charge Voltage
Velocity Angular velocity Current
Mass Moment of inertia Inductance Capacitance
Spring constant Torsion constant Elastance Susceptance
Damping Rotational friction Resistance Conductance
Drive force Drive torque
Undamped resonant frequency :
Differential equation:
M\ddot x + \gamma\dot x + Kx = F\,

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