Relaxation in classical systems

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The discussion centers on the concept of relaxation phenomena in classical systems, particularly using the example of a damped oscillator. It highlights the significance of relaxation time, which affects how quickly a system returns to equilibrium, and mentions exponential decay in motion equations. Participants seek clarification on the implications of varying relaxation times and inquire about non-exponential terms in relaxation phenomena. The terms "overdamped," "underdamped," and "critically damped" are introduced as relevant concepts in understanding system behavior. Overall, the conversation aims to deepen the understanding of relaxation dynamics in physical systems.
James Starligh
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Dear all,

I'd like to specify meaning othe relaxation phenomenon on example in some classical system.
For example in Wiki I found example of dampled oscilator where the relaxation time ( the time is needed for the system to return to the equilibrium fluctuation pattern) add exponential decay to the motion equation of such oscilator

http://en.wikipedia.org/wiki/Relaxation_(physics)#Mechanics:_Damped_unforced_oscillator


Could some one provide me more quatinely what with such system will be expected in case of increasing (decreasing) of the relaxation time ? What are the examples of the non-exponential terms in different relaxation phenomena?

James
 
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