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

## Question:

An oscillating mass has a period of 0.89 s and a mass of 4.19 kg. What is the spring constant k (in units of N/m) of the string?

## Spring Mass System:

To stretch a spring or to compress a spring we need to apply some force. The force required to stretch or compress a spring by unit length is known as the spring constant. For the given spring-mass system we have to calculate the spring constant.

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.

Practice Applying Spring Constant Formulas

from

Chapter 17 / Lesson 11
3.1K

In this lesson, you'll have the chance to practice using the spring constant formula. The lesson includes four problems of medium difficulty involving a variety of real-life applications.