For a particle executing simple harmonic motion with amplitude and angular frequency
PHYSICS · Multi-part · A Level · Physics · Further mechanics and thermal physics · Further mechanics and thermal physics
Problem
For a particle executing simple harmonic motion with amplitude A and angular frequency ω, let E denote the total mechanical energy of the oscillation.
(i) Derive an expression for the magnitude of displacement when the kinetic energy is one–quarter of the total mechanical energy.
(ii) If the motion starts from the mean position at t=0, determine the smallest positive time at which the kinetic energy becomes one–quarter of the total energy.
(iii) Prove that the average values of kinetic and potential energies over the first half of a complete oscillation are equal.