Question

A 16 kg mass suspended from a light spring is replaced by a 4 kg mass. What factor changes the frequency of the oscillation? (a) 1/4
(b) 2.0
(c) 4.0
(d) 1/2
(e) does not change

Answer 1

Answer:

Frequency change by a factor of 2.

(b) is correct option.

Explanation:

Given that,

Mass = 16 kg

Replaced mass = 4 kg

We need to calculate the frequency

Using formula of frequency  

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

Put the value into the formula

$f_{1}=\dfrac{1}{2\pi}\sqrt{\dfrac{k}{16}}$

$f_{1}=\dfrac{1}{2\pi}\dfrac{\sqrt{k}}{4}}$....(I)

$f_{2}=\dfrac{1}{2\pi}\sqrt{\dfrac{k}{4}}$

$f_{2}=\dfrac{1}{2\pi}\dfrac{\sqrt{k}}{2}}$...(II)

$f_{2}=2f_{1}$

Hence, Frequency change by a factor of 2.