Which of the following is not essential for SHM

[silent10]

Which of the following is not essential for SHM?
a) restoring force
b) gravity
c) elasticity
d) inertia

 

[Doc Al]

Which of the following is not essential for SHM?
a) restoring force
b) gravity
c) elasticity
d) inertia

What do you think and why?

 

[silent10]

I think its gravity
Simple harmonic motion requires a restoring force, as that brings the objects back to the equilibrium position. It requires inertia, as that keeps the object moving through equilibrium, resulting in harmonic motion. It requires elasticity, as that is the source of the restoring force, it's the 'k' value, as it were. Elasticity results in the spring constant. Gravity, however, is not necessary. While it may be necessary for pendulum harmonic motion, as it results in the restoring force there, simple harmonic motion can be just a ball on a spring resting on a horizontal frictionless table. Pull the ball, it will have simple harmonic motion until the end of time, with no gravity acting on it.

 

[Doc Al]

Good answer!

Edit: Oops! See gneill's correction.

 

[gneill]

Where's the elasticity in a pendulum?

 

[phinds]

Where's the elasticity in a pendulum?

That's beside the point. The question was which of these can you omit and still HAVE SHM, not "are there any of these that would break SLM in SOME cases".

 

[gneill]

That's beside the point. The question was which of these can you omit and still HAVE SHM, not "are there any of these that would break SLM in SOME cases".

The question is, "which is not essential for SHM". Do pendulums exhibit SHM? Is there elasticity in the pendulum system? If your answers are "yes" and "no" respectively, then elasticity is not essential for SHM.

 

[Doc Al]

Where's the elasticity in a pendulum?

Good point, gneill. (You devil, you! )

 

[ardie]

its a stupid A level question, that's why there's no completely correct answer. I would say the correct pick would be inertia

 

[silent10]

So its elasticity for a simple pendulum and gravity for a horizontal spring system.

 

[Doc Al]

So its elasticity for a simple pendulum and gravity for a horizontal spring system.

Evaluate each choice by asking: Is it possible to have SHM without this?

 

[ehild]

Pendulum motion is not really shm, but there are cases for shm where elasticity is not essential.

ehild

 

[I like Serena]

Hmm, I thought the motion of a pendulum is not SHM.
It is only SHM by approximation. :)

However, motion by elasticity does show SHM.

Edit: I think answer (c) should be: elasticity-like force, since that is required and not contained in the other answers.

 

[ardie]

Pendulum motion is not really shm, but there are cases for shm where elasticity is not essential.

ehild

:O
you sure u didnt just have a really bad day or one of ur friends died or something?

 

[ardie]

sure if u have a really stiff spring it will also not undergo SHM no matter how hard u press

 

[gneill]

For small angular displacements the motion of a pendulum approximates very closely to SHM, and it is often taken as such in introductory level courses. I judged that this would be the case given the apparent level of this question and the forum it's posted in... I am, of course, always open to corrections

 

[ardie]

The fact that it is Simple only means it is valid to some approximation. The fact that it is harmonic motion applies to pendulums, springs, car breaks, anything of the kind. but not all of them are simple. pendulums motions are SHM, as discovered first by galile.
inertia is not required for SHM because light is the most important case of SHM and it has no inertia. otherwise gravity, elasticity or restoring forces are all encountered in SHM systems as essentials parts contributing to the motion being harmonic.

 

[I like Serena]

inertia is not required for SHM because light is the most important case of SHM and it has no inertia.

Yeah, so the answer should be "inertia-like behavior", which is required and not contained in the other answers.
But then, it's only an A level question.

And no, as you can find in for instance the http://en.wikipedia.org/wiki/Simple_harmonic_motion" , simple harmonic motion does not mean it is simple by approximation.

 

[ardie]

in deriving the equation of motion for simple harmonic oscillators, one takes the assumption that F=-kx
where k is the constant of proportionality that connects the motion of the particle to the rigidity of the oscillator. this assumption, that the rigidity of the oscillator is constant is the reason why you call it a simple system, because you are ignoring the second and higher order terms in rigidity. otherwise the word simple will take no meaning whatsoever
as you can see here
http://galileo.phys.virginia.edu/classes/152.mf1i.spring02/Oscillations2.htm
or else in any textbook, you can see that in general F does not equal a constant but also depend on dx/dt. which is why the word simple implies an approximation to a system where there is no damping, or second order torque terms as well as higher order rigidity terms.

 

[ehild]

:O
you sure u didnt just have a really bad day or one of ur friends died or something?

??

Consider the case of a floating box in water when it is pushed a bit downward from its equilibrium position and released.

Consider the case of a body falling in a tunnel drilled across the Earth through its centre. (well, not quite practical example)

These are mechanical examples for shm without elasticity.

ehild

 

[ehild]

Edit: I think answer (c) should be: elasticity-like force, since that is required and not contained in the other answers.

What do you mean on elasticity-like force? A restoring one?

ehild

 

[I like Serena]

What do you mean on elasticity-like force? A restoring one?

ehild

No, a linear one. :)

As opposed to for instance an inverse square one.

 

[ehild]

No, a linear one. :)

As opposed to for instance an inverse square one.

That is why the ions of an ionic crystal, affected by inverse square and even higher order repulsive forces perform shm around their equilibrium position (well, approximately, while the resultant restoring force is about proportional to the displacement)

ehild

 

[ehild]

For small angular displacements the motion of a pendulum approximates very closely to SHM,

It depends on what we consider very close. The differential equation for the mathematical pendulum is
d²θ/dt²=-g/l sin(θ)
and at 10° angular displacement sin(θ) and θ (in radians) differ by 0.001.

ehild

 

[Redbelly98]

A real spring & mass is also just an approximation to SHM.

Is it possible to have more than one correct answer here?

 

[Doc Al]

Is it possible to have more than one correct answer here?

I certainly think so.

 

[Dadface]

A real spring & mass is also just an approximation to SHM.

Is it possible to have more than one correct answer here?

Exactly.The question asked "which of the following" not which one of the following.
None of the mechanical systems studied at A level move exactly with SHM,they move approximately with SHM.For a simple pendulum to move with SHM the bob would need to be of zero size,the string would need to be weightless and the amplitude zero.Expressing it differently,to move with SHM it mustn't move.:tongue:

 

[phinds]

The question is, "which is not essential for SHM". Do pendulums exhibit SHM? Is there elasticity in the pendulum system? If your answers are "yes" and "no" respectively, then elasticity is not essential for SHM.

You were thinkly more clearly here than I was. Thanks for pointing that out. I need to pay more attention.