(a) Show that the time required for a particle executing simple harmonic motion with…

PHYSICS · Subjective · A Level · Physics · Further mechanics and thermal physics · Further mechanics and thermal physics

Problem

(a) Show that the time required for a particle executing simple harmonic motion with amplitude

A

and angular frequency

\omega

to travel from displacement

x_1

x_2

(

x_2>x_1>0

) while moving away from the mean position is

t=\frac{1}{\omega}\left[\sin^{-1}\left(\frac{x_2}{A}\right)-\sin^{-1}\left(\frac{x_1}{A}\right)\right].

(b) Using the result of part (a), determine the time taken when

A=4.0\,\text{cm}

x_1=1.0\,\text{cm}

x_2=3.0\,\text{cm}

and the period of oscillation is

1.5\,\text{s}