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

PHYSICS · Subjective · 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 an ideal horizontal spring of force constant

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

. The positive

x

–axis is taken towards the right from the equilibrium position. (i) At

t = 0

the block is

0.040\,\text{m}

to the right of equilibrium and moving leftwards with speed

0.60\,\text{m}\,\text{s}^{-1}

. Find the amplitude

A

of its motion. (ii) Determine the initial phase

\phi

(restrict your answer to

-\pi < \phi \le \pi

) of the motion. (iii) Hence write the complete equation

x(t)

of the displacement using the cosine form. (iv) Calculate the earliest time after

t = 0

when the block first reaches the extreme right position. (v) State the magnitude of the maximum acceleration of the block.