Question

If an object of mass m attached to a light spring is replaced by one of mass 9m, the frequency of the vibrating system changes by what factor? (a)$\frac{1}{9}$ (b)$\frac{1}{3}$(c) 3.0 (d) 9.0 (e) 6.0.

Short answer

Increasing the mass by a factor of 9 will decrease the frequency to $\frac{1}{3}$of its original value, answer is (b)

Step-by-step solution

Simple Harmonic Motion

When an object undergoes simple harmonic motion, frequency of oscillation may be written as

$f=\frac{\omega }{2\pi }=\frac{1}{2\pi }\sqrt{\frac{k}{m}}$

$f=$Frequency of oscillation

$\omega =$Angular frequency

$m=$Mass of object

Find the frequency of the vibrating system

The frequency of vibration is

$f=\frac{\omega }{2\pi }=\frac{1}{2\pi }\sqrt{\frac{k}{m}}......\left(1\right)$

Thus, from equation (1), increasing the mass by a factor of 9 will decrease the frequency to$\frac{1}{3}$ of its original value.