Question

A spring has a force constant of 80 N/m it vibrates with the frequency of 7 Hz. Calculate the period, angular frequency and mass of the spring

Answer 1

a)

$$T=\dfrac{1}{f}=\dfrac{1}{7\ Hz}=0.143\ s.$$

b)

$$\omega=2\pi f=2\pi\cdot7\ Hz=43.96\ \dfrac{rad}{s}.$$

c)

$$\omega=\sqrt{\dfrac{k}{m}},$$ $$m=\dfrac{k}{\omega^2}=\dfrac{80\ \dfrac{N}{m}}{(43.96\ \dfrac{rad}{s})^2}=0.041\ kg.$$