An oscillating mass has a period of 0.89 s and a mass of 4.19 kg. What is the spring constant k...

The time period of an oscillating mass system is given by

$$\begin{align} T=2\pi\sqrt{\dfrac mk} \end{align} $$

This is the formula all we need to solve the problem.

Given:

• Time period, {eq}T=0.89\ \rm s {/eq}

• Mass, {eq}m=4.19\ \rm kg {/eq}

Required:

• Spring constant, {eq}k=? {/eq}

Using the formula we get:

$$\begin{align} &T=2\pi\sqrt{\dfrac mk}\\[.3 cm] &k=\dfrac{4\pi^2m}{T^2}\\[.3 cm] &k=\dfrac{4\pi^2(4.1\ \rm kg)}{(0.89\ \rm s)^2}\\[.3 cm] &\color{blue}{\boxed{k\approx 204\ \rm N/m}} \end{align} $$

Hence, the spring constant of the spring is 204 N/m.