TITLE:
Delay Harmonic Oscillator
AUTHORS:
Philipp Kornreich
KEYWORDS:
Lagrangian, Equation of Motion, Hamiltonian, Delay, Oscillation
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.6 No.7,
July
12,
2018
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.