Question

A body of mass $1kg$ is made to oscillate on a spring of force constant $16N/m.$ Calculate:

1.angular frequency.

2.the frequency of vibration.

Answer 1

We have,

$m=1$ kg, $K=16$ N/m

$\omega =\sqrt{\frac{K}{m}}$ for a S.H.M

$=\sqrt{\frac{16}{1}}=4$ rad/s

Also,

$\omega =2\pi n\Rightarrow n=\frac{\omega }{2\pi }=\frac{4}{2\pi }=\frac{2}{\pi }$ Hz.

$\therefore n=\frac{2}{3.14}=0.6369$ Hz.

The angular frequency of the body is $4$rad/s and the frequency of vibration is $0.6369$ Hz.

Hence, this is the answer.