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Elastic Potential Energy and SMH

  • Thread starter Roze
  • Start date
14
0
1. Homework Statement
A simple harmonic oscillator has a total energy E.
a) Determine the kinetic and potential energies when the displacement is one half the amplitude.
b) For what value of the displacement does the kinetic energy equal the potential energy?


2. Homework Equations
PEs= 1/2Kx^2
KE = 1/2mv^2


3. The Attempt at a Solution

I actually have the solution given to me, but I don't understand some of the steps.

We know that x=A/2, so:
PEs= 1/2K(A/2) which we can expand to K/8A^2

Then they say that: K/8A^2 = K/8(2E/K) and this is the part I'm confused about. Why does A^2=2E/K?

Thanks!
 

Answers and Replies

Doc Al
Mentor
44,827
1,083
Hint: Express the total energy (E) in terms of amplitude. (At what point is the energy purely PE?)
 
14
0
When x=0?
 
Doc Al
Mentor
44,827
1,083

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