A particle executes simple harmonic motion with amplitude and period .

PHYSICS · Multi-part · A Level · Physics · Further mechanics and thermal physics · Further mechanics and thermal physics

Problem

A particle executes simple harmonic motion with amplitude

A

and period

T

. (i) Derive an expression for the ratio of its instantaneous kinetic energy

K

to potential energy

U

at a displacement

x

from equilibrium. (ii) Hence obtain the displacement (expressed as a fraction of

A

) at which

K

equals

U

. (iii) For a particle of mass

0.25\,\text{kg}

executing such motion with amplitude

0.20\,\text{m}

and angular frequency

16\,\text{rad}\,\text{s}^{-1}

, calculate the common value of

K

and

U

at the displacement found in part (ii).