The equation
is known as the universal oscillator equation since all second order linear oscillatory systems can be reduced to this form. This is done through nondimensionalization.
If the forcing function is f(t) = cos(ωt) = cos(ωtcτ) = cos(ωτ), where ω = ωtc, the equation becomes
The solution to this differential equation contains two parts, the "transient" and the "steady state".
Read more about this topic: Harmonic Oscillator
Famous quotes containing the words universal and/or equation:
“There is an universal tendency among mankind to conceive all beings like themselves, and to transfer to every object, those qualities, with which they are familiarly acquainted, and of which they are intimately conscious. We find human faces in the moon, armies in the clouds; and by a natural propensity, if not corrected by experience and reflection, ascribe malice or good-will to every thing, that hurts or pleases us.”
—David Hume (1711–1776)
“A nation fights well in proportion to the amount of men and materials it has. And the other equation is that the individual soldier in that army is a more effective soldier the poorer his standard of living has been in the past.”
—Norman Mailer (b. 1923)