# When the displacement in SHM is 0.4 times the amplitude A, what fraction of the total energy is...

## Question:

When the displacement in SHM is 0.4 times the amplitude A, what fraction of the total energy is kinetic energy? What fraction of the total energy is potential energy? At what displacement, in terms of the amplitude, is the energy of the system half kinetic energy and half potential energy?

## Spring Potential Energy:

An object oscillating at the end of a spring has a speed that is constantly changing, and therefore a kinetic energy that is constantly changing. It must be stored as potential energy somewhere in the system.

The energy stored in a spring (or any other system that acts as a simple harmonic oscillator) is called spring potential energy. The amount of potential energy a distance {eq}x {/eq} from the equilibrium position is:

{eq}U = \frac{1}{2}kx^2 {/eq}.

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We can answer this question using the spring potential energy formula:

{eq}U = \frac{1}{2}kx^2 {/eq}.

The total energy of this object is the sum of...

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.