Driven Harmonic Oscillator

In summary, a driven harmonic oscillator is a physical system that undergoes periodic motion due to an external driving force. The equation of motion for a driven harmonic oscillator is m&middot;x&Prime; + k&middot;x = F<sub>0</sub> sin(&omega;t), where m is the mass, k is the spring constant, x is the displacement, F<sub>0</sub> is the amplitude of the driving force, and &omega; is the angular frequency. The driving force can amplify or dampen the oscillation, depending on the frequency. The resonance frequency of a driven harmonic oscillator is equal to the natural frequency, &omega;<sub>r</sub> = &radic;(k
  • #1
Tom1
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  • #2
Can you figure out the forces working on a part of the oscillator?
 
  • #3
The driving force just seems to be a function of angular frequency.
 
  • #4
Why have you deleted the original post? It is both annoying and counter-productive, how do you expect us to help you if we can't see the question?
 

1. What is a driven harmonic oscillator?

A driven harmonic oscillator is a physical system that undergoes periodic motion or oscillation due to the application of an external driving force or input. Examples of driven harmonic oscillators include a simple pendulum, a mass-spring system, or an LC circuit.

2. What is the equation of motion for a driven harmonic oscillator?

The equation of motion for a driven harmonic oscillator is given by:

m·x″ + k·x = F0 sin(ωt)

where m is the mass of the oscillator, k is the spring constant, x is the displacement from equilibrium, F0 is the amplitude of the driving force, and ω is the angular frequency of the driving force.

3. How does the driving force affect the motion of a driven harmonic oscillator?

The driving force can either amplify or dampen the oscillation of a driven harmonic oscillator, depending on the frequency of the driving force. If the frequency of the driving force matches the natural frequency of the oscillator, resonance occurs and the amplitude of the oscillation increases. However, if the frequency of the driving force is significantly different from the natural frequency, the amplitude of the oscillation decreases due to damping.

4. What is the resonance frequency of a driven harmonic oscillator?

The resonance frequency of a driven harmonic oscillator is equal to the natural frequency of the oscillator and is given by:

ωr = √(k/m)

where k is the spring constant and m is the mass of the oscillator.

5. How does damping affect the motion of a driven harmonic oscillator?

Damping is a force that opposes the motion of a driven harmonic oscillator and causes the oscillation to gradually decrease in amplitude. The amount of damping is determined by the damping coefficient, which can be either underdamped, critically damped, or overdamped. Underdamped oscillators continue to oscillate with decreasing amplitude, critically damped oscillators return to equilibrium the fastest, and overdamped oscillators take the longest to return to equilibrium.

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