Help with oscillating spring concept?

[riseofphoenix]

Is it acceleration?

I found this graph online:

Would the answer be acceleration?

 

[Doc Al]

Would the answer be acceleration?

Yes, but what's your reasoning?

 

[riseofphoenix]

Yes, but what's your reasoning?

Based on the graph: when v = 0, the mass has no kinetic energy, KE = ½mv². Therefore, all of its energy is in the form of elastic potential energy, PE_elastic = ½kx². When PE_elastic is maximum, the restoring force within the spring is also maximized. This results in the mass' acceleration to be maximized as the spring acts to return the mass to its equilibrium position.

 

[riseofphoenix]

Yes, but what's your reasoning?

What about this one...number 2:

τ_net = Iαα = angular acceleration = v/r
I = moment of inertia = mr²

Is the answer center of gravity

 

[riseofphoenix]

Yes, but what's your reasoning?

Because I don't think center of gravity has anything to do with it...

 

[Doc Al]

Based on the graph: when v = 0, the mass has no kinetic energy, KE = ½mv². Therefore, all of its energy is in the form of elastic potential energy, PE_elastic = ½kx². When PE_elastic is maximum, the restoring force within the spring is also maximized. This results in the mass' acceleration to be maximized as the spring acts to return the mass to its equilibrium position.

Good. Another way to look at it is in terms of Hooke's law. The restoring force--and thus the acceleration--is maximum when the displacement from equilibrium is maximum.

 

[Doc Al]

What about this one...number 2:

τ_net = Iα

This is what you need. If the net torque is constant, what can you say about alpha?

 

[riseofphoenix]

This is what you need. If the net torque is constant, what can you say about alpha?

With respect to I (moment of inertia) you mean?

 

[Doc Al]

With respect to I (moment of inertia) you mean?

I think we can safely assume that the moment of inertia of the object is constant.

 

[riseofphoenix]

I think we can safely assume that the moment of inertia of the object is constant.

So angular acceleration will not be constant but will be changing.

 

[Doc Al]

So angular acceleration will not be constant but will be changing.

How did you determine that? Look back at that equation.

 

[riseofphoenix]

How did you determine that? Look back at that equation.

Oh...

I'm not sure. I guessed...
Cause I remember for the Conservation of Angular Momentum concept,

L = Iω

If L is to stay constant, then when you increase I, ω decreases. And if you decrease I, ω increases.

I thought it was a similar concept with this question - the whole inverse relationship.

 

[riseofphoenix]

Wait so you're saying if the net torque is constant, then BOTH I (moment of inertia) and alpha (angular acceleration) are constant.

 

[Doc Al]

Conservation of angular momentum has nothing to do with this one.

Imagine if instead of torque, the problem said that there was a constant net force on the object. What would you conclude then?

 

[Doc Al]

Wait so you're saying if the net torque is constant, then BOTH I (moment of inertia) and alpha (angular acceleration) are constant.

Well we can assume that the object doesn't change its moment of inertia (otherwise the problem is silly). The key conclusion is that alpha is constant (and non-zero). And what does that tell you?

 

[riseofphoenix]

Conservation of angular momentum has nothing to do with this one.

Imagine if instead of torque, the problem said that there was a constant net force on the object. What would you conclude then?

Oh!

F = ma... So a constant F means a constant acceleration a. Which means, constant non-zero acceleration.

Velocity is changing?

 

[Doc Al]

F = ma... So a constant F means a constant acceleration a.

Right.

Which means, if a = 0, then velocity is non-zero.

No, it means that if a = some non-zero value, then velocity is changing.

So in this case, angular velocity would be changing when α (angular acceleration) is constant.

Good!

 

[riseofphoenix]

Right.

No, it means that if a = some non-zero value, then velocity is changing.

Good!

So the answer is angular velocity...


Thanks for the clarification!

 

[riseofphoenix]

I have one more quick question!

 

[riseofphoenix]

This may be a really obvious question but...
is it the highest frequency, 740 Hz?

 

[Doc Al]

This may be a really obvious question but...
is it the highest frequency, 740 Hz?

Once again I must ask: What is your reasoning? (What does it mean to be a harmonic of some fundamental frequency?)

 

[riseofphoenix]

Once again I must ask: What is your reasoning? (What does it mean to be a harmonic of some fundamental frequency?)

Oh wait...this is what I found online

"A 'harmonic' is defined as an integer multiple of a the fundamental frequency F. Harmonics of F will have frequencies NF where N is an integer. The case where N = 1 is the fundamental frequency itself.

So in the example we are given, we should look at the frequencies 100, 200, 250, etc and try to find the highest value of F for which all of the given frequencies are integer multiples. Clearly this is 50Hz:-

100 = 2*50 (second harmonic of 50Hz)
200 = 4*50 (4th harmonic)
250 = 5*50 (5th harmonic)
300 = 6*50 (6th harmonic)

In principle it is possible that the fundamental could be 25Hz or 5Hz or even 2Hz, but if any of these were the case we would expect that there would be harmonics such as 275Hz (11*25) or 280 (56*5), etc, but we are told that these are not observed.

It seems likely therefore that the fundamental is 50Hz"


So essentially, to find the harmonics (using the fundamental frequency of 160 Hz), all I have to do is divide each option by 160 to see if it gives me an integer.

540/160 = 3.375
740/160 = 4.625
640/160 = 4 Is this the answer?
440/160 = 2.75

Note to self:

The frequency (f) of the nth harmonic (where n represents the harmonic # of any of the harmonics) is n times the frequency of the first harmonic. In equation form, this can be written as:

f_n = n • f₁

 

[Doc Al]

So essentially, to find the highest harmonic (using the fundamental frequency of 160 Hz), all I have to do is divide each option by 160 to see if it gives me an integer.

540/160 = 3.375
740/160 = 4.625
640/160 = 4 Is this the answer?
440/160 = 2.75

Good!

(Nit pick: You're not finding the highest harmonic, just a higher harmonic. The 640 Hz is the only harmonic in the bunch. In this case it's the 4th harmonic.)

 

[riseofphoenix]

Good!

(Nit pick: You're not finding the highest harmonic, just a higher harmonic. The 640 Hz is the only harmonic in the bunch. In this case it's the 4th harmonic.)

Sorry I took so long to respond I was trying to finish dinner as fast as i could...
And ok - so the answer is 640 Hz (even though the 4th harmonic is the only harmonic in the choices I'm given)

Thanks for taking the time to answer my questions!