Calculating Damped Oscillation Frequency: 1-(8π²n²)-1

[yukcream]

if the amplitude of a damped oscillation is decrease to 1/e after n periods, how can i show that the frequency is about [1-(8pi^2n^2)-1]times the frequency of undamped ocillations? can i assume that the oscillation is critical damping such that the term b/2m and k/m can be cancel in the expression of the damped frequency and natural freuency relation?

thanks for attention!

yukyuk

 

[Physics Monkey]

You know the damping factor and the modified period in terms of the undamped period and the damping constant. You should probably start by evaluating the damping factor after n periods and setting it equal to 1/e.

 

[yukcream]

To physics monkey,

Thanks for your help but i cannot understand what you mean? how can i write out the relation between the damped period and undamped~ quite confusing ! Also why I start by evaluating the damping factor after n periods and setting it equal to 1/e?

yuk

 

[Physics Monkey]

yukcream,

No problem, please look here http://hyperphysics.phy-astr.gsu.edu/HBASE/oscda.html to clarify for yourself what the various terms mean.