Will a SHM eventually reach zero displacement or not?

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SUMMARY

In the context of simple harmonic motion (SHM), a damped system will eventually reach zero displacement due to energy loss from friction and surrounding interactions. Theoretical models suggest that while displacement decreases over time, it never actually reaches zero in ideal conditions. Specifically, underdamped oscillations decrease exponentially according to the formula e^(-kt), indicating that displacement approaches zero but never fully attains it. This distinction is crucial for understanding the behavior of oscillatory systems in real-world applications.

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  • Understanding of simple harmonic motion (SHM)
  • Familiarity with damping in oscillatory systems
  • Knowledge of exponential decay functions
  • Basic principles of thermodynamics related to energy loss
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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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