A block of mass is attached to a horizontal ideal spring of force constant

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

Problem

A block of mass

0.50\,\text{kg}

is attached to a horizontal ideal spring of force constant

200\,\text{N\,m}^{-1}

. It performs simple harmonic oscillations on a friction-free surface with amplitude

0.10\,\text{m}

. (i) Derive an expression for the instantaneous speed

v

of the block in terms of its displacement

x

, amplitude

A

and angular frequency

\omega

. (ii) Using the result of part (i), calculate the speed of the block when its displacement from the equilibrium position is

0.060\,\text{m}

. (iii) Determine the ratio of kinetic energy to potential energy of the block at the same displacement.