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Damped Oscillation 
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#1
Jan2908, 08:36 AM

P: 3

1. The problem statement, all variables and given/known data
A damped oscillator of mass m=1,6 kg and spring constant s=20N/m has a damped frequency of \omega' that is 99% of the undamped frequency \omega. As found out by me: The damping constant b is 0.796 kg/s. Q of the system is 7.1066 kg^1. Are the units here right? The questions are: a) Confirm that the system is lightly damped. b) What new damping constant b_new is required to make the system critically damped? c) Using b_new calculate the displacement of the mass at t=1,0s given that the displacement is zero and the velocity is 5,0 m/s at t=0. 2. Relevant equations To calculate b I used \omega' = ( \omega^2  b/2m)^1/2 To calculate Q I used Q = ((mass*spring constant)^1/2)/b 3. The attempt at a solution I couldn't find any specific definition of when a system is lightly damped. I found somewhere that if \omega' is about equal to \omega the system is lightly damped, which is the case here (\omega' = 99%\omega) but this can't be the answer since I have to find a new damping constant. If I had the new damping constant I would just use the given data to make up a wave equation for x(t). Thanks for helping. 


#2
Jan3108, 05:01 PM

HW Helper
P: 1,539

Hope that helps. 


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