Simple Harmonic motion; please help ! THANKS?

Question

Your boss at the Cut-Rate Cuckoo Clock Company asks you what would happen to the frequency of the angular SHM of the balance wheel if it had the same density and the same coil spring (thus the same torsion constant), but all the balance wheel dimensions were made one-third as great to save material.

1a.]By what factor would the frequency change?

1b.]Would the frequency increase or decrease by the factor found in part (1a)?

2a.] By what factor would the torsion constant need to be changed to make the smaller balance wheel oscillate at the original frequency?

2b.]Would the torsion constant need to be increased or decreased by the factor found in part (2a)?


Note: I realize that this question was posted and someone has answered, but it is not the correct solution.
For comparison, the link is :
http://answers.yahoo.com/question/index;_ylt=AgtVN2FFPxkM4fGBUVxza2cjzKIX?qid=20070313104823AA3BdER


Help is much appreciated :]

Answer 1

Ok, it's a SHM, the frequency in a SHM, is known by :

F = 1/2pi*sqrt(K / I)

F = frequency

K = constant

I = moment of inertia

For the whell, the momen of inertio will be = M*R^2

Let's consider ir as a rim ok, if it's a disk, then the moment of inertia will be : 1/2*MR^2

the balance wheel dimensions were made one-third, then :
the dimension will be : R/3

I = M/R^2 / 9

the first frequency :

F = 1/2pi*sqrt(K / M*R^2)

new frequency = F' = 1/2pi*sqrt(K / M*R^2/9) =3/2pi*sqrt(K/MR^2)

F' = 3/2*F

the old frequency F = 2/3F'

b) The frequency will increase

c) the new frequency : 1/2pi*sqrt(K / MR^2/9)

= 1/2pisqrt(3k / MR^2), if we want this new frequency yo change and be the old frequency, the constant k, must be :

k/3, so the constant must be one - third it was.

d) It need to decrease three times.

Hope that helped

Answer 2

i could say the respond is D, vibration all human beings understand besides is obviously around, and in physics w=2*pi/f, f= frequency, so which you will't use hertz as w isn't a unit of frequency, its the unit of angular frequency that's fairly different regardless of the reality that they are even nevertheless heavily appropriate, w is likewise used in around action to discover the angular speed at each and each time so as which could helps D too,, no longer between distinctive suggestions make any adventure and are pointless, A is indoors the bin by way of actuality hz is a appropriate unit for frequency, B is faulty by way of actuality a link between diplacement and time exists already that's v=d/t, C cant be precise by way of actuality w has no longer something to do with mass prefer this helps you on your quest