Simple Harmonic Motion question.

[gabloammar]

Homework Statement

Explain why the motion of someone jumping up and down on a trampoline is not simple harmonic motion. (Their feet lose contact with the trampoline during each bounce.)


2. The attempt at a solution

I really can't think of anything. Maybe I haven't completely understood the concept of s.h.m. If someone could point me to a place where I could understand the whole thing.


Thanks!

 

[Morgoth]

F=-kx
is that true?

 

[gabloammar]

I don't think the negative sign is there, but I don't need a calculated answer. I need a theoretical one.

 

[Morgoth]

if there was no - then being on the positive x, would mean it would be pushed away forever.
well it has to do with how you define the - + signs.
http://ocw.mit.edu/courses/physics/8-01-physics-i-classical-mechanics-fall-1999/video-lectures/lecture-10/
the theoritical one says that it doesn't follow the law of F=-kx. the item oscillating should always feel a force proportional to its displacement. The one jumbing on a trampoline has no force on him while he is on air.

 

[gabloammar]

Ah, sorry. As I said, I think I never understood the concept of this topic really well, just started like 4 hours ago.

And the book says, 'The restoring force is not proportional to the distance from the equilibrium point, when the person is not in contact with the trampoline the restoring force is equal to the person's weight which is constant.' Is that the same thing you just said?

 

[Morgoth]

well yes... I just didn't take in consideration the weight force :) Since I assumed it constant on air but on the trampoline too.
However if there was a hole on Earth (so the gravitational force would not be equal to a constant but would depend on r distance from the equilibrium point/center of the earth), leading to its anti-diametrical side, the law of gravity would make the human oscilate from one side of the Earth to the other, and all the way back.

 

[gabloammar]

Well let's not just drill a hole in the Earth for the question's sake xD

Though, then, the answer to this question would be that because the restoring force is constant once the person is not in contact with the trampoline [the constant force being the person's weight], the requirement for s.h.m that is that the force must be directly proportional to the displacement, doesn't apply anymore, so we can't classify this as s.h.m. Would this be correct?

 

[Morgoth]

your book already gives the answer

 

[gabloammar]

I know I know but I need to elongate that in a good, acceptable way or my teacher won't accept it. In any case at least I understood when you helped me :) thanks a lot!

 

[Morgoth]

providing straightforward answers is recognised as cheating and is against the rules. Since you understood, you have to find the right way to type it.

 

[BlueFish]

I would have said something different, just from thinking about it. A person jumping on a trampoline is not (to me) simple harmonic motion because it is not continuous for either system. Or, in other words, if you take the person as one system and the trampoline as the second system, you must prove that one of them is moving with shm, right? Well, the trampoline is not moving with shm because after the person is no longer in contact with the trampoline (in the air) the trampoline is shuddering at a much faster rate, and then the person comes in contact with it again. This is also happening to the person, but in a more subtle way. The person is traveling on one curve up and down in the air, out of contact with the trampoline. Then the person transfers some of their energy to the trampoline. In order to regain the same curve as before, the person has to put energy into the system again because the trampoline only gives back a portion of the energy given to it.

So, in either case, the curve of the motion is disjointed and discontinuous, and simple harmonic motion is continuous and can only be approximated in low friction systems where energy can be assumed to be conserved over short time periods, if I am remembering my physics labs correctly.

 

[Morgoth]

not quite correct. For example my example with the Earth's gravity above. you don't really need something oscilating to create shm. The force should just be one "returning" you in the initial point, and that's how you can work.
For example by the time Hooke's law stops working you stop having shm, and instead you get the complete deformation