A particle executes 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

A particle executes simple harmonic motion with amplitude

0.05\,\text{m}

and angular frequency

8\pi\,\text{rad s}^{-1}

. It starts from the equilibrium position moving towards the positive extreme at

t=0

. (i) Write the equation for the displacement

x(t)

. (ii) Determine the earliest time (after

t=0

) at which the displacement becomes

0.025\,\text{m}

. (iii) Find the magnitude of the velocity and acceleration of the particle at the instant calculated in part (ii).