Will a SHM eventually reach zero displacement or not?

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    Displacement Shm Zero
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Discussion Overview

The discussion centers around whether simple harmonic motion (SHM) will eventually reach zero displacement, considering both theoretical and real-world scenarios, including damped and underdamped oscillations.

Discussion Character

  • Debate/contested, Conceptual clarification, Technical explanation

Main Points Raised

  • One participant questions if a theoretically ideal SHM will eventually reach zero displacement, suggesting that in a damped system, amplitude and frequency decrease over time.
  • Another participant argues that in real-world scenarios with friction and energy loss, SHM will reach a point where displacement effectively becomes zero due to random thermal motion.
  • A third participant inquires specifically about underdamped oscillation, asking if displacement would only approach zero theoretically.
  • A later reply explains that in underdamped SHM, displacement decreases exponentially but will never technically reach zero due to the nature of the exponential decay.

Areas of Agreement / Disagreement

Participants express differing views on whether SHM can reach zero displacement, with some suggesting it can in real-world conditions while others maintain that theoretical models indicate it will never reach zero.

Contextual Notes

The discussion highlights assumptions regarding energy loss, the nature of damping, and the implications of theoretical versus real-world models, which remain unresolved.

linyen416
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THEORETICALLY will a SHM eventually reach zero displacemtn or not?



If it is DAMPED, amplitude would decrease with time, as would frequency, but would they would reach zero wouldn't they?
 
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In the real world with friction and energy lost to the surrounding, yes it will reach zero displacement. Or rather it will reach a point where the random thermal motion is the same as the background.
In simple physics models you assume the loss in energy is proportional to the displacement and so in theory it would never reach zero. In the same way that a theoretical cup of coffee would never cool down to room temperature - because cooling rate is proportional to the temperature difference.
 


mgb,
thanks for ur input!

im wondering about underdamped oscillation as well. would displacement theoretically ONLY APPROACH zero?
 
Hi,

in an underdamped shm, the motion decreases by the factor e^(-kt), where k is the frictional force and t is time. as this is a decreasing exponential it will never techniquelly reach zero.
 

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