anonymous
  • anonymous
HELPU! Per definition; cos(w' 2T) is always equal to one. Why? There is no explanation to why it will always be one. How can w'2T always result into one? ( Attachment )
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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schrodinger
  • schrodinger
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anonymous
  • anonymous
anonymous
  • anonymous
I asked the same question here ( http://openstudy.com/study#/updates/55e571ede4b03567e110d72b ) and got an answer; but realized that w is derived! How can a derived w' cancel out a w?
Kainui
  • Kainui
Ok well I looked at the question you asked and that was short and sweet and makes perfect sense so there's not much I can really say about that. One thing though that might help though is this: \[\cos(x) = \cos( x+ 2 \pi)\] But we could do this any number of times, so really: \[\cos(x)=\cos(x+n2 \pi)\] If we evaluate this at x=0 what do we have? \[\cos(0)=\cos(n 2 \pi)\]\[1=\cos(n 2 \pi)\] So it looks like here in your problem you have n=2 possibly? \[1=\cos(4 \pi)\]

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anonymous
  • anonymous
@Kainui I understand that; but not in this case, when we have a w' 2pi inside. As w can be different; we dont really know it will always be result into 1. Now if w was not w', it would make perfect sense mathematically; as it would just become n2pi, as you mentioned. However w' cannot cancel out w (I believe), so it does not mathematically make sense
Kainui
  • Kainui
I don't know what the difference is between \(\omega\) and \(\omega'\) is since I don't know where they came from.
Kainui
  • Kainui
Like I am particularly suspicious that you might be blindly using formulas that apply to one certain case and trying to apply them generally.
anonymous
  • anonymous
w = root(k/m) w' = root(k/m - b^2/4m^2) Their values should not matter, as, according to previous answer (link in previous post) they should cancel eachother out; resulting into an cos(n*2pi) value resulting into it always becoming = 1
anonymous
  • anonymous
(or rather; the values of k, m, and so on) - the variables matter of course!
Kainui
  • Kainui
Where does \(\frac{-b^2}{4m^2}\) come from?
anonymous
  • anonymous
No idea - Its from a formula book
Kainui
  • Kainui
There's your problem
anonymous
  • anonymous
It might be dampening, hmm
anonymous
  • anonymous
Thanks for helping! Ill ask the teacher if I can get a hold of him :)
Kainui
  • Kainui
Yeah for all you know \(\omega = \omega'\)
Kainui
  • Kainui
That is to say: \[T = \frac{2 \pi}{\omega'}\] Is totally possible, you don't know.
anonymous
  • anonymous
Then it would make perfect sense; yes :) Ill look further into it
baru
  • baru
if the confusion is over w and w', w' isnt the derivative of w, w and w' are used to represent undamped natural frequency and damped frequency
baru
  • baru
\[T=2 \pi \sqrt{ \frac{m}{k}}\] this is the time period for the undamped system, you cannot substitute it here since you have damping 'b'

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