simple harmonic motion

[chiddler]

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(EK 724) Which of the following is equal to the frequency of the wave on a string:
where Δx = "it oscillates distance Δx"

Image

A. v/Δx
B. 1/Δx * sqrt(T/&#956😉
C. 1/2pi * sqrt(k/m)
D. v/A

i forgot answer. it's C.

 

[MedPR]

C, but only because I have it memorized since it's mentioned in TBR.

Wish I could help more 🙁

 

[chiddler]

C, but only because I have it memorized since it's mentioned in TBR.

Wish I could help more 🙁

thanks its np. is it just a formula to memorize? or is this derived somehow?

 

[TopPops]

formula should be omega = sqrt k/m

omega is also 2 pi f. So make f the subject.

 

[MedPR]

thanks its np. is it just a formula to memorize? or is this derived somehow?

I'm sure TBR derived it somehow, I don't have the book with me though.

 

[chiddler]

formula should be omega = sqrt k/m

omega is also 2 pi f. So make f the subject.

FJLEAJ:FEALKFE

I KNEW THAT

holy crap

:'(

how did i miss this!

thank you

 

[milski]

The derivation comes from F=ma and F=kΔx. That gives you a differential equation for x which you then 'solve.' Either memorize it or know what the frequency depends on and be able to reason what it is.

 

[MedPR]

where did omega=2pi*f come from?

 

[chiddler]

where did omega=2pi*f come from?

i remember it from class

omega = 2pi*f = 2*pi / T = sqrt(k/m)

 

[MedPR]

i remember it from class

omega = 2pi*f = 2*pi / T = sqrt(k/m)

Well that's good to know! Thank you.

 

[milski]

where did omega=2pi*f come from?

omega^2=k/m is a substitution that is done to make the solution of the differential equation a bit more presentable. You end up with:

x=A cos(omega * t + fi)

If you take into account that cosine is periodic with period 2pi, you get omega * (t+T) - omega * t = 2pi or T = 2pi/omega or omega = 2pi/T = 2pi * f.

T is the period of the harmonic motion, f is the frequency.

And typing formulas here really sucks.

 

[MrNeuro]

omega^2=k/m is a substitution that is done to make the solution of the differential equation a bit more presentable. You end up with:

x=A cos(omega * t + fi)

If you take into account that cosine is periodic with period 2pi, you get omega * (t+T) - omega * t = 2pi or T = 2pi/omega or omega = 2pi/T = 2pi * f.

T is the period of the harmonic motion, f is the frequency.

And typing formulas here really sucks.

umm so is the point of this question that the frequency of the string here is independent of the tension on the string that in fact is just the frequency of the spring??

and why do you care about omega (angular velocity??)

 

[milski]

umm so is the point of this question that the frequency of the string here is independent of the tension on the string that in fact is just the frequency of the spring??

That has to be a typo in the original question - either from chiddler or from the source. Answer C is the correct answer for a sPring. The correct formula for the fundamental frequency of a sTring is 1/(2L)*sqrt(T/miu) and that's not on the list. But you are correct that it will depend on the tension of the string.

and why do you care about omega (angular velocity??)

omega in this case called angular frequency. You don't have to use it but it makes for an easier formula to remember.