Question

A spring with a spring constant of 165 N/m is attached to a 2.0 kg mass and set into motion.

Answer 1

Explanation:

We have,

Spring constant of the spring, k = 165 N/m

Mass, m = 2 kg

It is required to find the period of the mass-spring system. For the spring mass system, the period is given by :

$T=2\pi \sqrt{\dfrac{m}{k} }\\\\T=2\pi \sqrt{\dfrac{2}{165} }\\\\T=0.69\ s$

The frequency of vibration is reciprocal of its time period. So,

$f=\dfrac{1}{T}\\\\f=\dfrac{1}{0.69}\\\\f=1.44\ Hz$

So, the period of the mass-spring system is 0.69 s and frequency is 1.44 Hz.