and Periods of a Relativistic Oscillator
relativistic oscillator is modeled on a computer. Two cases are considered:
(1) The mass is independent of the speed [m(v)=m0] and (2) The mass
is a function of the speed [m(v)=m0/(1-v2/c2)1/2].
We begin by noting
that the period of oscillation of a mass on a spring is independent
of the massí maximum speed when the mass is a constant of the motion (i.e.
when the mass always equals m0).
In this article we
compute the motions of an oscillator when the maximum speed of the mass is a
relativistic 2.9e8 meters/second.
Computation for the two cases mentioned in the abstract are performed.
The oscillator in
each case can be considered itself to be a clock. Successive ticks can be
defined to be each time the mass passes through x=0 when traveling in the
The Python program
that computes the Amplitude and period of oscillation in each case is provided
in Appendix A. The results are as follows.
Amplitude=2.90e8 meters, Period=6.28 seconds.
Amplitude=7.23e8 meters, Period=11.36 seconds.
It is clear that both
the amplitudes and periods of the oscillator increase when the dependence of
mass on speed is factored in.
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program computes the period of a 'clock', which consists of a mass,
to an ideal spring of spring consfant k.
mass oscillates back and forth on the end of the spring.
mass' speed, at x=0 and t=0, is maximum and relativistic. Thus x=0 is the center
The first of four legs of oscillation is assumed to end when the
speed is approximately zero. The goal of the modeling program is to compute the
the period of oscillation in two cases: (1) when the mass is independent of its
(2) when the mass is a function of its speed.
#Speed of light
#Maximum of mass speed (at x=0 and t=0)
#Time between computation loops
#Initial position of mass
#Case 1. Choose this for non-relativistic mass
#Un-comment this for relativistic mass
#Spring force on mass
#Acceleration of mass
#Time at beginning of oscillation
for first quarter of oscillation
#Uncomment this for relativistic mass.