Question

A spring has a force constant of 80 N/m, it vibrates with a frequency of 7 Hz.

Calculate the,

a)period

b)angular frequency

c) mass of the spring

Answer 1

a)

$$T=\dfrac{1}{f}=\dfrac{1}{7\ Hz}=0.14\ s.$$

b)

$$\omega=\dfrac{2\pi}{T}=\dfrac{2\pi}{0.14\ s}=44.8\ \dfrac{rad}{s}.$$

c)

$$\omega=\sqrt{\dfrac{k}{m}},$$ $$m=\dfrac{k}{\omega^2}=\dfrac{80\ \dfrac{N}{m}}{(44.8\ \dfrac{rad}{s})^2}=0.04\ kg.$$