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GR9677 #8 |
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Problem
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This problem is still being typed. |
Mechanics }Damped Oscillations
One should remember that damped oscillations have decreasing amplitude according to an exponential envelope. As the amplitude shrinks, the period increases. The additional force instated in the problem is equivalent to damping, and thus the period increases, as in choice (A).
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Alternate Solutions |
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Comments |
cobrachi
2008-10-31 22:14:48 | It's simple to think of this conceptually. The new force is in the opposite direction of the velocity so it will act against the motion of the particle. Thus, it decreases the angular frequency and since T=2pi/w --> a smaller w results in a larger T. |  | greenfruit
2008-10-31 08:36:12 | Question about the soln: Why can we conclude that as amplitude shrinks period increases? | | gn0m0n
2008-10-20 01:22:45 | To echo a couple of questions and hopefully clarify them: do we mean that the period is greater than when it was undamped (ie, but still constant once it is damped) or do we mean it is changing in time once the damping is applied?
gn0m0n
2008-10-20 01:24:19 |
I'd like to ask the same thing about the amplitude.
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| | sharpstones
2007-04-02 19:45:51 | Just to tex it out. The general solution to a damped oscillator is:  where  where  is the damping term and  is the frequency of the solution
if omega is real (which is the underdamped case:  ) you will have oscillations which do in fact have a constant period but will have decreasing amplitude from the  . clearly the frequency  will be less then the original frequency  so the period will be greater.
sharpstones
2007-04-02 19:46:55 |
that should be 
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blah22
2008-02-14 11:02:07 |
I'm confused. Why do you say you will have oscillations which have a constant period and in the next sentence say the frequency will clearly be less?
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| | huanggyellow
2007-03-20 07:28:47 | How about choice (E)? Surely the period is constantly changing (increasing)?
mhas035
2007-03-21 21:42:23 |
The frequency of an underdamped oscillator is omega = omega{undamped}*sqrt(1-b.^2/4mk), i.e. smaller than the undamped frequency, and constant.
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