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## Homework Statement

The amplitude of simple harmonic oscillation is A = 10 cm. Find a displacement x when K = 1/6 U. Here K is a kinetic energy and U is a potential energy.

## Homework Equations

[tex]KE = \frac{1}{2} k A^2[/tex]

[tex]U = \frac{1}{2} k x^2[/tex]

## The Attempt at a Solution

I'm not sure the correct method of doing this problem but here is what I have attempted based on an example from my notes:

[tex]KE = \frac{1}{6} U[/tex]

[tex]\frac{1}{2} k A^2 = \frac{1}{6} \frac{1}{2} k x^2[/tex]

[tex]A^2 = \frac{1}{6} x^2[/tex]

[tex](0.1)^2 = \frac{1}{6} x^2[/tex]

[tex]x \approx 0.24 m[/tex]