Kentai
2009-11-05 22:08:52 | with the equation change from x'' = -w^2 to x'' = -bx' - w^2 x, w must become smaller to compensate the -bx' term, hence the period increase. |  |
jmason86
2009-10-04 13:26:22 | No one has addressed the other options that ETS gives us. I thought that (D) was correct because of limits. If b--> that implies an infinite force acting against the oscillator, which I would imagine would completely destroy the period because it would just stop moving. If b-->0 then you have no damping effect at all and it should behave like an ideal SHO with a period of  .
Why is this not correct?!
kroner
2009-10-09 19:27:03 |
The period does increase with increasing b, but it's not a linear relationship. See the formula provided by sharpstones below.
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phun_lover
2009-09-29 17:56:23 | This question is somewhat confusing since a damped oscillator doesn't have a well-defined period, in the sense that it's position isn't a periodic function of time. However, it's position can be written as a decaying exponential times a periodic function (if the damping is in the correct range), and so what they want here is the period of that periodic factor--easily solved for from the corresponding differential equation. | |
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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gt2009
2009-06-28 13:20:30 |
Both periods are constant, but the damped period is greater than the undamped period.
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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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