A particle of mass is attached to a horizontal ideal spring and performs simple…
PHYSICS · Subjective · A Level · Physics · Further mechanics and thermal physics · Further mechanics and thermal physics
Problem
A particle of mass m is attached to a horizontal ideal spring and performs simple harmonic motion (SHM) of amplitude A on a smooth table.
(i) State the expression for its total mechanical energy in terms of the spring constant k and amplitude A.
(ii) Starting from the definition of kinetic energy and the restoring force of the spring, obtain expressions for its instantaneous kinetic energy and potential energy when the particle is at a displacement x from the mean position.
(iii) Explain, with reasons, how these two forms of energy vary as the particle moves from x=−A to x=+A. Identify the points where each form of energy attains its maximum value.
(iv) Sketch, on the same set of axes, qualitative graphs of kinetic energy and potential energy versus displacement x over one complete oscillation from −A to +A.