|Jan29-08, 08:36 AM||#1|
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.
|Jan31-08, 05:01 PM||#2|
Hope that helps.
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