Question

A 5 kg mass is oscillating on a spring with a time period of 2.8 seconds. What is the spring constant k of the spring?

Answer 1

k = 25.18 N/m

Step-by-step explanation:

Simple Harmonic Oscillator

It consists of a weight attached to one end of a spring being allowed to move forth and back.

If m is the mass of the weight and k is the constant of the spring, the period of the oscillation is given by:

`\displaystyle T=2\pi {\sqrt {\frac {m}{k}}}`

If the period is known, we can find the value of the constant by solving for k:

`\displaystyle k=m\left((2\pi)/(T)\right)^2`

Substituting the given values m=5 Kg and T=2.8 seconds:

`\displaystyle k=5 \left((2\pi)/(2.8)\right)^2`

k = 25.18 N/m