Washer101 said: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.
Simple Harmonic Motion at Relativistic Speeds is a type of motion in which an object moves back and forth in a regular pattern at speeds close to the speed of light. This motion is characterized by a restoring force that is proportional to the displacement of the object from its equilibrium position.
Simple Harmonic Motion at Relativistic Speeds is different from regular Simple Harmonic Motion in that it takes into account the effects of relativity, specifically time dilation and length contraction, which occur at high speeds. This means that the period and amplitude of the motion may be different from what is expected in regular Simple Harmonic Motion.
The equation for calculating the period of Simple Harmonic Motion at Relativistic Speeds is T = 2πγ/ω, where T is the period, γ is the Lorentz factor, and ω is the angular frequency. This equation takes into account the effects of relativity on the motion.
No, Simple Harmonic Motion cannot occur at speeds faster than the speed of light. According to the theory of relativity, the speed of light is the maximum speed at which any object can travel. Therefore, any motion, including Simple Harmonic Motion, cannot occur at speeds faster than the speed of light.
One example of Simple Harmonic Motion at Relativistic Speeds is a particle moving through a particle accelerator. Another example is the motion of a charged particle in a uniform magnetic field. These types of motion are often observed in high-energy physics experiments.