Distinguished Oscillations of a Forced Harmonic Oscillator

Distinguished Oscillations of a Forced Harmonic Oscillator

Author(s): T.G. Proctor

The College Mathematics Journal, Vol. 26, No. 2 (Mar., 1995), pp. 111-117.

Published by: Mathematical Association of America

Stable URL: http://www.jstor.org/stable/2687362

Tags: Higher-order equations and linear systems, other topics in differential equations

Abstract: This paper does well to delve into how one can model, using differential equations, the changes that a harmonic oscillator experiences when outside forcing values affect it. The author first goes over how beats are formed in an oscillator, stating that the forcing frequency is different from the natural frequency, resulting in a beats vibration. They continue to resonance, where when a resonant function has a piece-wise function as the forcing term, how it would oscillate was dependent on a value of the variable $a$. From here they talked about how instead of a continuous forcing term, there was pulses much like pushing a child on a swing set. They determined that eventually the pulses would not add anything to the system as the oscillator would reach a maximum amplitude. In an oscillator with beats, they talked about what would happen if resistance was added to the oscillator. They eventually calculated that for any resistance greater than zero, the beats would eventually disappear. Throughout the paper they showed graphs, visualizing what would happen in each instance. Jonathan Burrows, Stephen. F. Austin State University, May 3, 2017.

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