Question

A body of unknown mass is attached to an ideal spring with force constant 120 N/m. It is found to vibrate with a frequency of 6.00 Hz. Find (a) the period; (b) the angular frequency; (c) the mass of the body.

Answer 1

Explanation:

Given that,

Force constant of the spring, k = 120 N/m

Frequency of vibration, f = 6 Hz

Solution,

(a) Let T is the time period of the spring. The relation between the frequency and the time period is given by :

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

$T=\dfrac{1}{6}$

T = 0.167 s

(b) Let $\omega$ is the angular frequency. It is given by :

$\omega=2\pi f$

$\omega=2\pi \times 6$

$\omega=37.69\ rad$

(c) The relation between angular frequency and the spring constant is given by :

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

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

$m=\dfrac{120}{(37.69)^2}$

m = 0.084 kg

or m = 84 grams

Therefore, it is the required solution.