Inquiry about Damped Oscillators

In summary, the conversation is about two inquiries related to analytical mechanics. One is about understanding the behavior of the full-width-half-maximum of the resonance of a forced and damped oscillator in relation to the Q-factor. The other is about whether the amplitude of a forced and damped harmonic oscillator becomes infinite at resonance. The participants also mention a helpful link to Wikipedia's page on Q factor, which contains expressions for damping and the relationship between bandwidth and Q.
  • #1
shanepitts
84
1
Hello,
I have two quick inquiries related to my studies on analytical mechanics.

The first is I don't quite fathom how a full-width-half-maximum of the resonance of a forced and damped oscillator behaves in relation to the Q-factor??

And the second is does the amplitude of a forced and damped harmonic oscillator become infinite at resonance? I know that when the frequency from both the force and damped oscillator are equal the damped oscillator become infinite but they do they both become infinite??

thanks
 
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  • #2
This came up in a thread a few weeks ago, but this link might be helpful since it contains some of the expressions for the damping and the relationship between bandwidth and Q:

Wikipedia on Q factor.
 

FAQ: Inquiry about Damped Oscillators

What is a damped oscillator?

A damped oscillator is a system that exhibits oscillatory motion, but with the amplitude of the oscillations decreasing over time due to the presence of a damping force. This damping force can be caused by factors such as friction or air resistance.

How does damping affect the motion of an oscillator?

Damping affects the motion of an oscillator by reducing the amplitude of the oscillations, causing them to gradually decrease in size. This can also change the frequency of the oscillations, making them slower or faster depending on the amount of damping present.

What is the equation for a damped oscillator?

The equation for a damped oscillator is: x(t) = Ae^(-bt)cos(ωt + φ), where x(t) is the displacement at time t, A is the initial amplitude, b is the damping coefficient, ω is the angular frequency, and φ is the phase angle.

How does the damping coefficient affect the motion of a damped oscillator?

The damping coefficient affects the motion of a damped oscillator by determining the rate at which the amplitude of the oscillations decreases. A larger damping coefficient means a faster decrease in amplitude, while a smaller damping coefficient means a slower decrease.

What are some real-life examples of damped oscillators?

Some real-life examples of damped oscillators include a swinging pendulum with air resistance, a car's suspension system, and a guitar string with a dampening device. Damped oscillators can also be found in electronic circuits and mechanical systems such as shock absorbers.

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