# Energy of an oscillating spring

1. Nov 7, 2009

### qazxsw11111

Ok, so I got a spring attached to a weight and positioned on the eqm point. So I displace it a little and it undergoes oscillation.

At the lowest point, everything is Elastic Potential Energy since extension is maximum.

At the eqm point, extension=0 so it is just a mixture of KE and GPE.

At the top, there is 0 KE, maximum GPE. But what about the Elastic Potential energy? Does the hooke's law extension formula includes 'compression'? Is there 'compression energy'?

Thanks.

2. Nov 7, 2009

### dotman

Yes, there is. The spring imparts a restoring force, and there is potential energy in this; if the spring is compressed, there is energy stored that can be used to accelerate (think in the pinball machine, how you shoot the ball). If the spring is extended, there is energy in that it wants to restore an attached object to equilibrium.

The potential energy is the same in either case, and is dependent only on the distance x from equilibrium (in either direction):

$$U = \frac{1}{2}kx^2$$

3. Nov 7, 2009

### qazxsw11111

Ok thanks. So the energy at the top is not purely GPE (although it is at maximum compared to other positions) but also maximum EPE (since maximum extension/compression)?

But what about conservation of energy?

Bottom: Elastic PE(max)
Top:Elastic PE(max)+GPE(max)

Im still quite confused lol.

4. Nov 8, 2009

### dotman

Well, let's take a minute and think about what's going on here, when you factor in gravity. The spring itself exerts a force on the attached mass-- upwards, if the mass is below equilibrium (spring is extended), and downwards, if the mass is above equilibrium (spring is compressed). Gravity, however, exerts a force downwards, always. So what's the net result? You get more force going down than you get going up. What does this mean in terms of motion of the mass? It means that it extends further from equilibrium at the downward portion, than it does when it compresses upwards (because of gravity).

So when you say Elastic PE(max), you have to note that the Elastic potential energy at the top of the motion is not equal to the elastic potential energy at the bottom (because of gravity).

Where does the extra energy go/come from? You guessed it, the gravitational potential energy. Energy is conserved.