(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

A particle is in simple harmonic motion along the x axis. The amplitude of the motion is xm.

When it is at x = x1, its kinetic energy is K = 5J and its potential energy (measured with U = 0 at x = 0) is U = 3J. When it is at x = –1/2xm, the kinetic and potential energies are:

A) K = 5J and U = 3J

B) K = 5J and U = –3J

C) K = 8J and U = 0

D) K = 0 and U = 8J

E) K = 0 and U = –8J

2. Relevant equations

[tex]

E = 1/2kA^2

[/tex]

[tex]1/2kA^2 = 1/2mv^2 + 1/2kx^2[/tex]

3. The attempt at a solution

[tex]

1/2kA^2 = 8[/tex]

[tex]1/2mv^2 + 1/2kx^2^ = 8[/tex]

[tex]A = 4/\sqrt{k}[/tex]

[tex]x = -1/2(4/\sqrt{k}) = -2/\sqrt{k}[/tex]

[tex]1/2mv^2 + 1/2k(-2/\sqrt{k})^2^ = 8[/tex]

[tex]1/2mv^2 + 2 = 8[/tex]

[tex]K = 6 J[/tex]

[tex]U = 8 - 6 = 2 J

[/tex]

As you see, this is not one of the choices. Am I doing something wrong?

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# Homework Help: Simple harmonic motion and energy - yet another answer key disagreement?

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