Question

A body of unknown mass is attached to an ideal spring with force constant 119 N/m . It is found to vibrate with a frequency of 6.35 Hz.

Find the period.

Find the angular frequency.

Find the mass of the body.

Answer 1

Mass of the body = m

Force constant of the ideal spring the body is attached to = k = 119 N/m

Frequency of the motion = f = 6.35 Hz

Time period of the motion = T

$T = \frac{1}{f}$

$T = \frac{1}{6.35}$

T = 0.157 sec

Angular frequency of the motion = $\omega$

$\omega = 2\pi f$

$\omega = 2\pi (6.35)$

$\omega$ = 39.9 rad/s

$\omega = \sqrt{\frac{k}{m}}$

Squaring both sides,

$\omega^{2} = \frac{k}{m}$

$m = \frac{k}{\omega^{2}}$

$m = \frac{119}{(39.9)^{2}}$

m = 0.0747 kg

a) Period of the motion = 0.157 sec

b) Angular frequency of the motion = 39.9 rad/s

c) Mass of the body = 0.0747 kg