Driven Oscillators: interesting cases?

In summary, the conversation discusses the need for interesting examples of driven, damped harmonic oscillators for a report. The person asks for suggestions, specifically excluding a driven mass-spring system and anything quantum-mechanical. Possible examples mentioned include a car shock absorber and resonance caused by an energy source, such as pushing a kid on a swing or the voice of Ella Fitzgerald. The person also considers using a piezoelectric crystal in an oscillator circuit as an example.
  • #1
radiogaga35
34
0
Hi there

I need some advice, please: can you suggest any interesting cases of a driven, damped harmonic oscillator? I need to write a report (part of some assignment) on the mathematical model/behaviour/etc. of some real-world driven oscillator.

No problems with the math, I'm just looking for an interesting model. By interesting I mean: not a driven mass-spring system! Also, I don't want to get into anything quantum-mechanical - it's not a physics assignment, and there's not really scope in the assignment to venture beyond a straightforward classical model.

An example might be some sort of car shock absorber, the "driven" part being on account of a bumpy road...presumably resonant oscillations would be undesirable! But any better suggestions?

Thank you!
 
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  • #2
"driven, damped harmonic oscillator" -- wouldn't that be just about any example of resonance that has an energy source?

Pushing a kid on a swing in the playground ... a piezoelectric crystal in an oscillator circuit ... the voice of Ella Fitzgerald breaks a glass in the TV commercial for Memorex recording tape ... every time a big truck goes by my house the beer mugs that I keep on top of my refrigerator go jingle-jingle ...

When you say "driven" I guess we can leave out the case of a tuning fork (or guitar string, etc.) that makes another one begin vibrating "in sympathy" -- I think in such cases that both oscillations are in exponential decay, so that's not a driven oscillation.
 
  • #3
Aha, thank you for your suggestions, I like the "Ella Fitzgerald" and piezoelectric crystal example. The former seems particularly fun, and a striking example of resonance...although I suppose it would be easier to study the effects of damping/different natural angular frequencies/etc. in the case of the piezoelectric crystal circuit, perhaps using mechanical analogues?
 

1. What is a driven oscillator?

A driven oscillator is a physical system that exhibits periodic motion under the influence of an external force or driving force. Examples include a mass on a spring, a pendulum, or an electronic circuit.

2. What are some interesting cases of driven oscillators?

Some interesting cases of driven oscillators include the harmonic oscillator, the damped oscillator, and the forced oscillator. The harmonic oscillator is the simplest case, where the restoring force is proportional to the displacement. The damped oscillator involves a dissipation factor that causes the amplitude of the oscillations to decrease over time. The forced oscillator is when the external driving force has a different frequency than the natural frequency of the oscillator, resulting in interesting phenomena such as resonance.

3. How is resonance related to driven oscillators?

Resonance is a phenomenon that occurs when a driven oscillator is subjected to an external force with a frequency that is close to its natural frequency. This results in the oscillator vibrating with a larger amplitude, and in some cases, the amplitude can become infinite. Resonance is important in many applications, such as in musical instruments and in electronic circuits.

4. Can driven oscillators exhibit chaotic behavior?

Yes, driven oscillators can exhibit chaotic behavior under certain conditions. Chaotic behavior is characterized by sensitivity to initial conditions, which means that even small changes in the initial conditions can result in vastly different outcomes. This can occur in driven oscillators when the external force is close to the natural frequency, leading to a phenomenon known as chaotic resonance.

5. How are driven oscillators used in real-world applications?

Driven oscillators have many practical applications in various fields. For example, they are used in mechanical engineering to dampen vibrations in buildings and bridges. In electrical engineering, driven oscillators are used in electronic circuits to generate signals of specific frequencies. They are also used in fields such as optics, acoustics, and atomic physics to study and understand various phenomena.

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