# Simple Harmonic motion : Is energy conserved

1. Apr 14, 2013

### hms.tech

1. The problem statement, all variables and given/known data

I doubt energy is conserved in SHM, or it might be possible that i be doing something wrong.
The particle (red dot) in the attachment is at its equilibrium position and oscillates with Simple Harmonic Motion between the two yellow colored plates.

Amplitude A = 1.5 m
Frequency = 3 Hz
Find the maximum speed of the particle
2. Relevant equations

Conservation of Energy
V = ω $\sqrt{A^{2}-x^{2}}$

3. The attempt at a solution

This max speed occurs at its equilibrium position .

V = 9∏ meters per second

2nd method (explain why this is wrong when it makes perfect sense)
Total energy at highest plate (yellow) = total energy at equilibrium position
mg(1.5) = 0.5m$v^{2}$
v = $\sqrt{30}$

What is wrong with energy conservation method ?

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Last edited: Apr 14, 2013
2. Apr 14, 2013

### voko

Without seeing the picture it is hard to say where you went wrong.

However, I should say that the second method seems inconsistent with either of the two typical SHM models. If the model is a pendulum, then the max height is not the amplitude. If the model is a spring with a mass, then I do not see any account of its stiffness.

3. Apr 14, 2013

### cepheid

Staff Emeritus
Yeah, what voko said. If this is a thing oscillating up and down on a spring, you're not accounting for the elastic potential energy due to that. If only gravity is acting, then the thing cannot be undergoing SHM.

4. Apr 14, 2013

### hms.tech

I thought i had uploaded it, sorry for that. Anyways, it is under gravity and it is going SHM. (why wouldn't it)

5. Apr 14, 2013

### voko

Is there a spring?

Or is it reflected upon colliding with either plate? Then there can't be any equilibrium between the plates.

6. Apr 14, 2013

### hms.tech

It is a needle which is being moved by an automated sewing machine

I really can't see why do you need that information to answer the question :
Why isn't Energy conserved in this problem ?
In ANY case, the total energy at each and every point (displacement) during the SHM must be the same

7. Apr 14, 2013

### voko

Because the gravitational energy is not the only kind of potential energy in this problem (for that matter, it is not even obvious that there is potential energy here). As cepheid said, gravity alone won't be enough for SHM in this case.

8. Apr 14, 2013

### technician

You quite correctly get max v = ωA = 9π
If you put this in the 0.5mv^2 expression you will get an expression for the max KE
The max PE is given by 0.5F x A (average force x max displacement)
If you substitute the expression for max force in SHM you should see that the max KE = Max PE

ps...I dont think has anything to do with gravitational PE, as the others have said this cannot be SHM if it simply bouncing between 2 plates, there must be a spring of some sort