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: | |||
 |
|||
Read more about this topic: Harmonic Oscillator
Famous quotes containing the words equivalent and/or systems:
“Inter-railers are the ambulatory equivalent of McDonalds, walking testimony to the erosion of French culture.”
—Alice Thompson (b. 1963)
“We have done scant justice to the reasonableness of cannibalism. There are in fact so many and such excellent motives possible to it that mankind has never been able to fit all of them into one universal scheme, and has accordingly contrived various diverse and contradictory systems the better to display its virtues.”
—Ruth Benedict (1887–1948)