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:
“The poor, stupid, free American citizen! Free to starve, free to tramp the highways of this great country, he enjoys universal suffrage, and by that right, he has forged chains around his limbs. The reward that he receives is stringent labor laws prohibiting the right of boycott, of picketing, of everything, except the right to be robbed of the fruits of his labor.”
—Emma Goldman (1869–1940)
“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)