Elastic Potential Energy and SMH

AI Thread Summary
In the discussion about elastic potential energy and simple harmonic motion, the focus is on determining kinetic and potential energies at specific displacements in a simple harmonic oscillator. When the displacement is half the amplitude (x = A/2), the potential energy is calculated as PEs = 1/2K(A/2)^2, simplifying to K/8A^2. The confusion arises regarding the relationship between amplitude and total energy, specifically why A^2 equals 2E/K. The total energy E is expressed in terms of amplitude, leading to the conclusion that at maximum displacement, all energy is potential. The discussion emphasizes understanding these relationships to clarify the calculations involved.
Roze
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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?


Homework Equations


PEs= 1/2Kx^2
KE = 1/2mv^2


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!
 
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Hint: Express the total energy (E) in terms of amplitude. (At what point is the energy purely PE?)
 
When x=0?
 
Roze said:
When x=0?
What's the PE when x = 0?
 

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