Simple Harmonic Motion at Relativistic Speeds

[Washer101]

On The Student Room I saw a couple of guys looking at whether the rules for Simple Harmonic Motion at non-relativistic speeds (e.g. a = -w²y and so on) would work if the maximum velocity of the particle hits relativistic speeds.

Many Thanks
W101

 

[Mentz114]

No, you get a different set of differential equations whose non-linearity makes them difficult to solve. And that's all I know about it.

 

[bernhard.rothenstein]

On The Student Room I saw a couple of guys looking at whether the rules for Simple Harmonic Motion at non-relativistic speeds (e.g. a = -w²y and so on) would work if the maximum velocity of the particle hits relativistic speeds.

Many Thanks
Have a look at
Relativistic (an)harmonic oscillator
Moreau, William; Easther, Richard; Neutze, Richard
American Journal of Physics, Volume 62, Issue 6, pp. 531-535 (1994).

The relativistic extension of one-dimensional simple harmonic motion is developed in the Lagrangian formalism. The relativistic equations of motion are derived and solved analytically. The motion with respect to proper time is analyzed in terms of an effective potential energy. While the motion remains bounded and periodic, the effect of time dilation along the world line is to cause it to become anharmonic with the period increasing with amplitude and the curvature concentrated at the turning points.