# A spring has a spring stiffness constant, k, of 420 N/m. How much must this spring be stretched...

## Question:

A spring has a spring stiffness constant, k, of {eq}420\ N/m {/eq}. How much must this spring be stretched to store 30 J of potential energy?

## Spring-Mass System

The spring-mass system is a very good example fora simple harmonic system.

The frequency of oscillation of a mass attached to a spring is given by,

{eq}\nu=\frac{1}{2\pi}\sqrt{\frac{k}{m}} {/eq}

Where,

• {eq}k {/eq} is the force constant and
• {eq}m {/eq} is the mass attached.

The total energy of the mass is given by,

{eq}E=T+V=\frac{1}{2}mv^2+\frac{1}{2}kx^2=\frac{1}{2}ka^2 {/eq}

Where,

• {eq}a {/eq} is the amplitude of oscillation,
• {eq}v {/eq} is the velocity of the mass and
• {eq}x {/eq} is the displacement from the equilibrium point.

The restoring force on the mass is given by,

{eq}F=kx {/eq}

## Answer and Explanation:

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#### Learn more about this topic: Hooke's Law & the Spring Constant: Definition & Equation

from

Chapter 4 / Lesson 19
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After watching this video, you will be able to explain what Hooke's Law is and use the equation for Hooke's Law to solve problems. A short quiz will follow.