The displacement of a particle executing simple harmonic motion is given by
PHYSICS · Multi-part · A Level · Physics · Further mechanics and thermal physics · Further mechanics and thermal physics
Problem
The displacement of a particle executing simple harmonic motion is given by x(t)=8cmcos(5t+6π), where t is in seconds. Consider one complete oscillation of the particle.
(i) Explain, without performing detailed calculations, how the kinetic energy and potential energy of the particle vary with time during one period.
(ii) Determine the instants within the first period at which the potential energy attains its maximum value. Give your answer in terms of fractions of the time period.
(iii) Draw qualitative sketches of the kinetic energy–time and potential energy–time graphs for one full period, clearly marking their maxima and minima.