# B Confusion About Oscillating Mass

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1. Jun 4, 2017

### person123

I'm sure there's an obvious answer to this, but this problem has been confusing me for some time.

Imagine there were a massive object attached to the end of a crankshaft. A force is applied to accelerate the crankshaft, causing the mass to oscillate. Assuming there is no friction, what would happen to the system when the force is no longer applied? It shouldn't be possible for it to slow down if there's no energy loss, but wouldn't it require a force to continue to accelerate the mass back and forth?

Last edited: Jun 4, 2017
2. Jun 4, 2017

### zwierz

picture is needed

3. Jun 4, 2017

### person123

I'm not exactly sure what you're looking for, but this is the basic idea.

4. Jun 4, 2017

### zwierz

the system will oscillate This is a Hamiltonian system with one degree of freedom

5. Jun 4, 2017

### person123

And it will continue to oscillate at the same rate even when the torque is no longer applied?

6. Jun 4, 2017

### zwierz

What does the "rate" mean? This will be nonlinear oscillation. Is gravity applied?

7. Jun 4, 2017

### person123

I mean the frequency of the oscillation of the mass. I don't understand what you're asking.

8. Jun 4, 2017

### zwierz

The motion of the system will be periodic

9. Jun 4, 2017

### Ibix

One thing to think about that may not have occurred to you - whatever your axle is attached to will also wobble so that the centre of mass does not move. This is analogous to the Earth-Moon system, which revolves around a point (the barycentre) slightly offset ftom the centre of the Earth.

Does that help?

10. Jun 4, 2017

### person123

I should have mentioned that. It would make sense not to include gravity just for the purpose of simplifying things, I suppose.

11. Jun 4, 2017

### zwierz

that is wrong
ok anyway the motion will be periodic

12. Jun 4, 2017

### Ibix

How is momentum conserved if the centre of mass moves?

13. Jun 4, 2017

### zwierz

who does say that momentum conserved?

14. Jun 4, 2017

### person123

How can momentum not be conserved? I assume that even if the mechanism were fixed on the earth, it would cause the earth to oscillate very slightly in response (as ibix described).

15. Jun 4, 2017

### zwierz

Oh if you include the Earth in the system then I withdraw my objections :)

16. Jun 4, 2017

### person123

I think that makes sense, but I still have one more question which relates to the initial purpose of this thread.
I was trying to calculate the torque required to oscillate the mass at a constant frequency. So I found the velocity of the mass, and I then found the derivative, which gave me the acceleration. This allowed me to find the torque at the point in which the velocity of the mass was zero and the acceleration was at its maximum. (It gave me τ=Mω^2l^2, in which l is the length of the short rod). However, it doesn't seem to make sense to calculate this when there isn't any torque required to maintain that constant oscillation. I can't seem to reconcile this confusion with the explanation.

Last edited: Jun 4, 2017
17. Jun 4, 2017

### A.T.

Are you assuming that all parts, except the block are masses? In that case the total energy is zero when the block is at rest, so the oscillation won't be maintained without an applied torque.

18. Jun 4, 2017

### person123

Yes, I'm assuming all other parts are without mass. Isn't that contradictory to ibix's argument, or is this just a misunderstanding on my part?

However, let's say the mass of the other parts were just extremely small. Would the frequency of oscillation decrease or remain constant over time?

Also, how can there be no energy in the system if it was initially in motion and no energy was lost?

19. Jun 4, 2017

### A.T.

Without energy dissipation, constant.

20. Jun 4, 2017

### person123

But can't you approximate what would occur in the system by considering the other parts without mass if the mass of those parts are in reality very small?

21. Jun 4, 2017

### A.T.

You have already answered this question, by pointing out the contradiction it leads to. How are massless rigid parts supposed to store energy, in order to conserve it, while the block stops at each turnaround?

22. Jun 4, 2017

### Ibix

The problem is that if nothing except the mass has mass then any forces applied cause infinite acceleration. You can certainly consider your crankshaft to be massless, but it has to be attached to something with mass in order for it to have been able to produce a torque in the first place without itself instantly spinning up to infinite speed.

23. Jun 4, 2017

### Nidum

I haven't quite locked on to what the problem is but let's try a few things :

The configuration is like that of a normal I/c engine . Crankshaft , connecting rod and notionally a piston . The piston has a large mass but the other components are massless . Conventional arrangements of bearings etc. but with zero friction .

If the crankshaft is initially rotated at constant rpm by an external power source then the piston will move back and forth in a straight line . Motion will be something like SHM but with some higher order motion components added .

When the external power source is disconnected the piston will continue to move until it reaches an extremity of it's travel where it will stop .

To make the motion continue beyond that stop point there needs to be a heavy flywheel fitted to the crankshaft .

24. Jun 4, 2017

### person123

I asked what would happen to the frequency of oscillation if the mass of the rods were extremely small.
According to A.T., ignoring friction, wouldn't any mass cause the oscillation to be maintained at a constant frequency?

25. Jun 4, 2017

### Nidum

I don't see any contradiction between what AT has said and what I have said .

When the external drive is disconnected the piston will just continue in motion until it can go no further . There is then no torque on the crankshaft to make it rotate and no force on the piston to start it moving again .

To make the motion keep going there needs to be enough residual rotational KE in the crankshaft to carry it past dead centre and then generate enough torque to produce a force in the connecting rod sufficient to start the piston moving again .

Zero mass crankshaft components can't store any KE at all .

In a real situation the crankshaft components themselves could be made sufficiently massive to store enough KE but more commonly the crankshaft components are kept relatively light and a massive flywheel is fitted instead .