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:
“This universal exhibition in Canada of the tools and sinews of war reminded me of the keeper of a menagerie showing his animals’ claws. It was the English leopard showing his claws.”
—Henry David Thoreau (1817–1862)
“Jail sentences have many functions, but one is surely to send a message about what our society abhors and what it values. This week, the equation was twofold: female infidelity twice as bad as male abuse, the life of a woman half as valuable as that of a man. The killing of the woman taken in adultery has a long history and survives today in many cultures. One of those is our own.”
—Anna Quindlen (b. 1952)