# Which of the following is not essential for SHM

1. Jun 26, 2011

### silent10

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

2. Jun 26, 2011

### Staff: Mentor

What do you think and why?

3. Jun 26, 2011

### 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.

4. Jun 26, 2011

### Staff: Mentor

Edit: Oops! See gneill's correction.

Last edited: Jun 26, 2011
5. Jun 26, 2011

### Staff: Mentor

Where's the elasticity in a pendulum?

6. Jun 26, 2011

### phinds

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".

7. Jun 26, 2011

### Staff: Mentor

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.

8. Jun 26, 2011

### Staff: Mentor

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

9. Jun 26, 2011

### ardie

its a stupid A level question, thats why theres no completely correct answer. I would say the correct pick would be inertia

10. Jun 26, 2011

### silent10

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

11. Jun 26, 2011

### Staff: Mentor

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

12. Jun 26, 2011

### ehild

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

ehild

13. Jun 26, 2011

### 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.

14. Jun 26, 2011

### ardie

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

15. Jun 26, 2011

### ardie

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

16. Jun 26, 2011

### Staff: Mentor

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

17. Jun 26, 2011

### 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.

18. Jun 26, 2011

### I like Serena

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" [Broken], simple harmonic motion does not mean it is simple by approximation.

Last edited by a moderator: May 5, 2017
19. Jun 26, 2011

### 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.

Last edited: Jun 26, 2011
20. Jun 26, 2011

### ehild

???????????

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