Explain the ratio of time scales, easy,

[INeedHelpTY]

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.

 

[fzero]

If there was no damping, what time scale would the spring constant define? Does it still define that in the presence of damping?