JAMP  Vol.6 No.7 , July 2018
Delay Harmonic Oscillator
Author(s) Philipp Kornreich1,2
ABSTRACT
The motion of two point objects at the end of a spring is analyzed. The objects interact by an elastic wave propagating through the spring. A new comprehensive method, Reaction Mechanics, for the analysis of this motion is used.  This analysis is valid when the propagation of the interaction through the spring wire takes less time than the period of the oscillating frequency. The propagation delay couples the oscillating and center of mass motions. If the masses are equal, the center of mass velocity is a constant, and the objects oscillate with a frequency which is a modification of the oscillation frequency with no delay. If the masses are not equal, the center of mass also oscillates. In the case of zero delay, the motion of the objects reverts to the motion of a Simple Harmonic Oscillator.
Cite this paper
Kornreich, P. (2018) Delay Harmonic Oscillator. Journal of Applied Mathematics and Physics, 6, 1425-1433. doi: 10.4236/jamp.2018.67119.
References
[1]   Achenbach, J.D. (1984) Wave Propagation in Elastic Solids. North Holland. Elsevier Science, Amsterdam.

[2]   Kornreich, P. (2017) Reaction Mechanics of Point Objects. Journal of Applied Mathematics and Physics, 5, 137-152.
https://doi.org/10.4236/jamp.2017.51015

[3]   Lavanayal, N., Rao Sampath, P. and Redd Promod, M. (2014) Design and Analysis of a Suspension Coil Spring for Automotive Vehicle. Journal of Engineering Research and Applications, 4, 151-157.

[4]   Goldstein, H. (1981) Classical Mechanics. 2nd Edition, Addison-Wesley Publishing Company, Boston.

 
 
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