A generalization of the phase relations in a forced harmonic oscillator

✍ Scribed by B.A. Fleishman

• Publisher: Elsevier Science
• Year: 1961
• Tongue: English
• Weight: 341 KB
• Volume: 272
• Category: Article
• ISSN: 0016-0032
• DOI: 10.1016/0016-0032(61)90037-0

✦ Synopsis

When a simple harmonic oscillator is subjected to a sinusoidally varying external force whose frequency is different from the natural frequency of the oscillator, there is a simple and well-known phase relation between the purely forced response and the forcing function.

They will have the same or opposite signs (except when both functions vanish) according as the forcing frequency is less or greater than the natural frequency.

It is shown here that when the sinusoidal forcing function is replaced by any member of a wide class of periodic functions, the relation between the signs of the forcing function and the forced response continues to hold when the forcing frequency is greater than the natural frequency, but no longer holds in the other case.