Explain the ratio of time scales, easy,

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SUMMARY

The discussion focuses on the interpretation of Beta, defined as Beta = b/sqrt(mk), as a ratio of time scales in the context of a damped spring system. The damping coefficient (b) represents the time scale for oscillation decay, while the spring constant (k) relates to the system's oscillation frequency. The time scales measure the rate of oscillation decay and the inherent oscillation period of the spring, respectively. The inquiry also addresses the implications of damping on the spring constant's time scale definition.

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Homework Statement



Beta = b/sqrt(mk)

Explain how Beta can be interpreted as a ratio of time scales. What do the time scales measure?

b: damping coefficient of spring (dimension: M/T)
m: mass attach to spring (dimension: M)
k: spring constant (dimension: M/T^2)


The Attempt at a Solution



To explain it, I just say that Beta can be shown to be the ratio of the Time in the Damping Coefficient to the Time in the Spring constant.

What the time scales measure are:
1) The time unit in the damping coefficient determines how fast the oscillation of the spring dies
2) The time unit in the Spring constant measures, i don't know about this.

I am totally not sure if i am answering this question right, thanks for the help.
 
Physics news on Phys.org
If there was no damping, what time scale would the spring constant define? Does it still define that in the presence of damping?
 

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