I am having problems figuring out how to get started with this one. A free dynamic system has a spring constant of 2Nm^-1 and a damping factor of 3 N-sec-m^-1. Determine the mass for which this system will be critically damped. I know k= 2Nm^-1 and c= 3 N-sec-m^-1 and roe= 2 *sqrt (k*m) is critically damped. Can someone please help me get started?
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Spring Question
- Thread starter sumrtym77
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D
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sumrtym77 said:I am having problems figuring out how to get started with this one. A free dynamic system has a spring constant of 2Nm^-1 and a damping factor of 3 N-sec-m^-1. Determine the mass for which this system will be critically damped. I know k= 2Nm^-1 and c= 3 N-sec-m^-1 and roe= 2 *sqrt (k*m) is critically damped. Can someone please help me get started?
Spring question from Sumrtym.... no wonder you can't get untracked.
You , first need to be careful regarding units a little bit in this problem. "m" in "k" and "c" is abbreviation for meters - but "m" in "roe" (it should be "ro" - not fish-eggs) is mass.
How is "ro" defined in your book?
When I studied vibration, damping ratio \(\displaystyle \xi\) was:
\(\displaystyle \xi = \frac{c}{2\sqrt{km}}\)
What is the condition for critical damping - the value of \(\displaystyle \xi\) - consult your text-book or do a google search.
If you are still stuck - write back showing your work - indicating exactly where you are stuck.
I have been banging my head in my physics book, calculus book, and de book (which isn't a very good one for explaining things) and I can't get anything started. Is the damping ratio something I need to find to get the mass or would I use the my"+ky'+cy=0 or not. I am so frustrated with this. I don't know what to do!
D
Deleted member 4993
Guest
sumrtym77 said:I have been banging my head in my physics book, calculus book, and de book (which isn't a very good one for explaining things) and I can't get anything started. Is the damping ratio something I need to find to get the mass or would I use the my"+ky'+cy=0 or not. I am so frustrated with this. I don't know what to do!
Go to:
http://www.efunda.com/formulae/vibratio ... damped.cfm
for a quick review.
Any calculus based physics book, where they discuss damped vibration - must deal with this topic. You are just not reading it carefully.
You don't need to use the DE - only find the dampening ratio (factor). It has a special value for critically damped system.