Oscillation:Resonant frequency in vacuum

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SUMMARY

The discussion centers on the concept of resonant frequency as it applies to a pendulum constructed with a light thread and a low-density polystyrene bob. When oscillated at its resonant frequency in a vacuum, the amplitude of the pendulum's motion tends to infinity due to the periodic application of force at the optimal timing. This phenomenon is analogous to pushing a swing at the precise moments to maximize amplitude without disrupting its motion. Understanding this principle is crucial for grasping the mechanics of oscillation and resonance.

PREREQUISITES
  • Understanding of basic physics concepts such as oscillation and periodic motion.
  • Familiarity with the principles of resonance and amplitude in mechanical systems.
  • Knowledge of pendulum dynamics and the factors affecting its motion.
  • Basic grasp of vacuum conditions and their impact on oscillatory systems.
NEXT STEPS
  • Study the mathematical derivation of resonant frequency in oscillatory systems.
  • Explore the effects of damping on oscillation and resonance.
  • Investigate the applications of resonance in engineering, such as in musical instruments or mechanical systems.
  • Learn about the differences between oscillation in air versus in a vacuum.
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This discussion is beneficial for physics students, educators, and anyone interested in the principles of oscillation and resonance, particularly in mechanical systems and their applications in real-world scenarios.

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Homework Statement


A pendulum is constructed from a fixed length of light thread and and a spherical,low density,polystyrene bob.It is forced to oscillate at a different frequencies in air,and the response is shown in the graph below.
363990__image527058.jpg


Homework Equations


The Attempt at a Solution



363990__image527062.jpg

This is the answer.I have googled it and still need explanation regarding how does ringing something at resonant frequency in vacuum causes the amplitude to tend to infinity.

Thanks for your help!
 
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Well that's basically what the resonant frequency is

Don't take this too literally as it's not quite the exact same thing, but to help understand resonance, let's say I'm pushing you on a swing. So I'm applying a periodic force at some frequency and you're oscillating back and forth. What happens if I apply the force too early while you're still coming back at me? Do I increase your amplitude? No you knock me on my butt. What if I wait too long? I fall on my face

But what if I apply the force at jussst the right time? I increase your amplitude. So if you're applying the force at just the right times (the resonant frequency) to the pendulum bob, you increase its amplitude every time without screwing up its own periodic motion, so it increases and increases
 

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