Simple Harmonic Oscillation of Balance Wheel in a Clock

[Hughng]

Homework Statement

The 900-mg balance wheel of a certain clock is made up of a thin metal ring of radius 12 mm connected by spokes of negligible mass to a fine suspension fiber as in (Figure 1) . The back-and-forth twisting of the fiber causes the wheel to move in simple harmonic motion with period T. The clock ticks four times each second, with the interval between ticks equal to T/2.

Homework Equations

I am not so sure how to approach this.

The Attempt at a Solution

I tried to find T. Since each seconds has four ticks and the time span between two is T/2, thus I inferred that 1 second = 3T/2 or T = 2/3 Second.
I know the formula for find K is T = 2*pi*sqrt (I/K), but I kept getting the wrong answer. Please help me out.

 

[TSny]

Hello and welcome to PF!

There is another way to interpret "The clock ticks four times each second". Let Δt be the time interval between two consecutive ticks. The statement "The clock ticks four times each second" could mean that there are four intervals Δt making up one second.

 

[Hughng]

Hello TSny,
I followed your guide and this is now I interpreted.
One interval Δt is equal to T/2. Then four of those are equal to 2T which is equal to 1 second. Then 1 T = 0.5 second.
With the correct answer to I = 1.3 * 10^-7 kg.m^2, and by applying the formula T = 2*pi*sqrt (I/K), I still get the wrong answer. This is getting tricky.

 

[TSny]

Uh oh. Sorry if I mislead you with an incorrect interpretation of the problem. What do you now get for K?

 

[Hughng]

I got 2.1*10^-5 (kg*m^2/s^2)

 

[TSny]

I got 2.1*10^-5 (kg*m^2/s^2)

That's what I get, too.

If we're making a mistake, hopefully someone will show us.

 

[Hughng]

Sure. Thanks TSny. I appreciate it.

 

[TSny]

If I don't round off until the end of the calculation, I get 2.0 x 10^-5. But I wouldn't think they are that picky with significant figures. Since you only have one more try, I would wait to see if someone else will either confirm what we are getting or else give us a hint as to where we are going wrong.

 

[Hughng]

It said incorrect dimension. I hate online homework.

 

[TSny]

What units did you enter? kg m²/ s² or Nm/rad. To me, these are essentially the same.

 

[Hughng]

The second one along with our answer of K, it said incorrect dimension.

 

[TSny]

The second one along with our answer of K, it said incorrect dimension.

I don't see why that's considered incorrect. I agree that online homework can sometimes be annoying.

 

[Hughng]

I don't see why that's considered incorrect. I agree that online homework can sometimes be annoying.

Here is the screenshot. So upsetting.

 

[TSny]

It could be an error in the online homework system. I'd bring it up with your instructor.

 

[Hughng]

If he cares, I will not go this far to post my homework online to ask for help. It is ok. We will figure it out. It is a 200-students class. He needs to rest.

 

[TSny]

If he cares, I will not go this far to post my homework online to ask for help. It is ok. We will figure it out. It is a 200-students class. He needs to rest.

All right. You have a good attitude. Best of luck with the rest of your homework.

 

[Hughng]

I have one more.

 

[TSny]

OK. You should post it as a new thread.

 

[Hughng]

OK. You should post it as a new thread.

You can take a look at a new question now. I am laughing at us right now. We should be in class together.