Magnitude of Displacement for Harmonic Oscillator

In summary, in order to find the magnitude of displacement when elastic potential energy equals kinetic energy, one must set the potential energy formula equal to the kinetic energy formula and solve for x, the displacement. This can be done by understanding the relationship between displacement and velocity, which are both functions of time in a harmonic oscillator.
  • #1
Dortega120
1
0

Homework Statement


A harmonic oscillator has angular frequency ω and amplitude A. What is the magnitude of the displacement when the elastic potential energy is equal to the kinetic energy? (Assume that U = 0 at equilibrium.)

Express your answer in terms of the variables ω and A.

Homework Equations



Potential Energy: U=(1/2)kx^2

Kinetic Energy: K= (1/2)mv^2

The Attempt at a Solution



Honestly, I don't really understand the question. What I was thinking had to be done at first was to set the PE formula equal to the KE formula, and then solve for x, which is the displacement.
 
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  • #2
Dortega120 said:

Homework Statement


A harmonic oscillator has angular frequency ω and amplitude A. What is the magnitude of the displacement when the elastic potential energy is equal to the kinetic energy? (Assume that U = 0 at equilibrium.)

Express your answer in terms of the variables ω and A.

Homework Equations



Potential Energy: U=(1/2)kx^2

Kinetic Energy: K= (1/2)mv^2

The Attempt at a Solution



Honestly, I don't really understand the question. What I was thinking had to be done at first was to set the PE formula equal to the KE formula, and then solve for x, which is the displacement.
That is right, set PE equal to KE and solve for x, in terms of the data given: angular frequency ω and amplitude A. But you need to know how the displacement and the velocity are related. Both are function of time What are these functions?

ehild
 

FAQ: Magnitude of Displacement for Harmonic Oscillator

What is the Magnitude of Displacement for Harmonic Oscillator?

The Magnitude of Displacement for Harmonic Oscillator is a measure of the distance traveled by an object in a periodic motion, such as a pendulum or a spring. It is calculated as the maximum distance from the equilibrium position to the furthest point reached by the object during its oscillation.

How is the Magnitude of Displacement related to the amplitude of a harmonic oscillator?

The Magnitude of Displacement and the amplitude of a harmonic oscillator are directly proportional. This means that as the amplitude increases, the magnitude of displacement also increases. The amplitude is a measure of the maximum displacement from the equilibrium position.

What factors affect the Magnitude of Displacement for Harmonic Oscillator?

The Magnitude of Displacement for Harmonic Oscillator is affected by the amplitude of the oscillation, the frequency of the oscillation, and the mass of the object. A larger amplitude or frequency will result in a larger magnitude of displacement, while a larger mass will result in a smaller magnitude of displacement.

How is the Magnitude of Displacement calculated mathematically?

The Magnitude of Displacement is calculated using the equation: D = A sin(ωt + φ), where D is the displacement, A is the amplitude, ω is the angular frequency, and φ is the phase angle. This equation takes into account the factors that affect the magnitude of displacement, such as amplitude and frequency.

What is the significance of the Magnitude of Displacement in harmonic motion?

The Magnitude of Displacement is an important quantity in the study of harmonic motion as it gives us information about the behavior of an object in a periodic motion. It is used to calculate the energy, velocity, and acceleration of the object, and can help us understand the stability and equilibrium of the system. Additionally, the Magnitude of Displacement can be used to determine the period and frequency of the oscillation.

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