Question

A spring with a constant of 100N/m vibrates at 25Hz. What is the frequency of vibration of a spring with a constant of 400N/m?

Answer 1

Given:

$k_1=100\:\rm N/m$

$f_1=25\:\rm Hz$

$k_2=400\:\rm N/m$

$f_2-?$

The frequency of vibration

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

Hence

$$f_2=f_1\sqrt{\frac{k_2}{k_1}}=2f_1=50\:\rm Hz$$