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:
“Perhaps basketball and poetry have just a few things in common, but the most important is the possibility of transcendence. The opposite is labor. In writing, every writer knows when he or she is laboring to achieve an effect. You want to get from here to there, but find yourself willing it, forcing it. The equivalent in basketball is aiming your shot, a kind of strained and usually ineffective purposefulness. What you want is to be in some kind of flow, each next moment a discovery.”
—Stephen Dunn (b. 1939)
“What avails it that you are a Christian, if you are not purer than the heathen, if you deny yourself no more, if you are not more religious? I know of many systems of religion esteemed heathenish whose precepts fill the reader with shame, and provoke him to new endeavors, though it be to the performance of rites merely.”
—Henry David Thoreau (1817–1862)