Question

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

What is the period of the mass-spring system?

What is the frequency of the vibration?

Answer 1

Step-by-step 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{(m)/(k) }\\\\T=2\pi \sqrt{(2)/(165) }\\\\T=0.69\ s`

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

`f=(1)/(T)\\\\f=(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.