Solve for Displacement in Harmonic Oscillator

In summary, The conversation is about finding the value of displacement where the kinetic energy equals the potential energy in a simple harmonic oscillator with total energy E=1/2kA^2. After some calculations, it is determined that the correct answer is x = (1/\sqrt{2}) A.
  • #1
flower76
51
0
Can someone check my work please I'm pretty sure I don't have the right answer but I can't figure out what I have wrong.

The question is:
A simple harmonic oscillator has total energy E=1/2kA^2
where A is the amplitude of oscillation.
For what value of the displacement does the kinetic energy equal the potential energy?

So I figure that if KE is equal to PE, then PE=1/2E

Therefore:

1/2kx^2 =1/2(1/2kA^2)
kx^2 = 1/2kA^2
x = 1/4A

Any ideas?
 
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  • #2
flower76 said:
So I figure that if KE is equal to PE, then PE=1/2E
Good.

Therefore:

1/2kx^2 =1/2(1/2kA^2)
Good.
kx^2 = 1/2kA^2
Good.
x = 1/4A
Not good. :grumpy:
 
  • #3
I think I see my error.

Is the answer x = 0.71A ?
 
  • #4
Yep. [itex]x = (1/\sqrt{2}) A[/itex]
 

1. What is displacement in a harmonic oscillator?

Displacement in a harmonic oscillator refers to the distance and direction of an object from its equilibrium position at a given time during oscillation. It is a measure of how far the object has moved from its starting point.

2. How is displacement calculated in a harmonic oscillator?

The displacement in a harmonic oscillator can be calculated using the equation: x = A*cos(ωt + φ), where x is the displacement, A is the amplitude, ω is the angular frequency, and φ is the phase angle. Alternatively, it can also be calculated using the equation: x = A*sin(ωt + φ).

3. What is the relationship between displacement and amplitude in a harmonic oscillator?

The amplitude of a harmonic oscillator is directly proportional to the maximum displacement of the object. This means that as the amplitude increases, the maximum displacement also increases. The amplitude also determines the maximum potential energy of the oscillator.

4. How does frequency affect displacement in a harmonic oscillator?

The frequency of a harmonic oscillator is directly proportional to the displacement. This means that as the frequency increases, the displacement also increases. This can be seen in the equation x = A*cos(ωt + φ), where ω is the angular frequency, and as it increases, the displacement increases as well.

5. How does mass affect displacement in a harmonic oscillator?

The mass of an object does not directly affect the displacement in a harmonic oscillator. However, it does affect the time period and frequency of the oscillation, which can indirectly influence the displacement. A higher mass will result in a longer time period and lower frequency, while a lower mass will result in a shorter time period and higher frequency.

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