# Spring energy conversions - help please

1. May 20, 2017

### xJJx

Hi guys, i'm currently trying to study the energy conversions of a spring - can someone tell me if my understanding of it is completely correct or not? Thank you so much! I made it as detailed as I could:

One complete oscillation of a spring: The spring starts off stationary, meaning it has no kinetic energy and no EPE, it only has GPE. As the spring is being deformed, it is gaining EPE and KE. The spring then reaches its maximum possible deformation; at this point, the spring has maximum EPE and zero KE. Once the deforming forces stop acting on the spring, it eventually returns back to its original shape; the spring oscillates towards its equilibrium position whilst all of its EPE is getting transferred into KE. At the equilibrium position, all of the springs EPE has now been transferred into KE, so the spring has maximum KE and zero EPE. The spring then oscillates towards its maximum possible deformation (the type of deformation is the opposite to its first type of deformation) whilst all of its KE is getting transferred into negative EPE. At the maximum possible deformation, all of the springs KE has now been transferred into negative EPE, so the spring has maximum negative EPE and zero KE. The spring then oscillates back towards its equilibrium position whilst all of its negative EPE is getting transferred into KE. At the equilibrium position, all of the springs EPE has now been transferred into KE, so the spring has maximum KE and zero EPE. The spring has now returned back to its original shape.

Last edited by a moderator: May 21, 2017
2. May 21, 2017

### AlphaLearner

You are mentioning GPE at beginning means that the block is hanging freely suspended by spring with one end attached to a rigid end. You have no used GPE anywhere in middle denotes that you were talking of block placed on floor with spring attached to it which is fixed to a rigid end. Be clear. Which system were you asking for? First case or second case? In first case, spring never lies in its original state because of gravity.

3. May 21, 2017

### Staff: Mentor

Are you talking about a spring that has mass (with no additional mass attached), or an ideal massless spring with a mass attached?

4. May 21, 2017

### AlphaLearner

Well, let me explain you the first case clearly.
First case: Block suspended freely with spring attached to it by one end and other end to a rigid support.
Consider spring to be massless.

Since there's gravity, the gravity tries to pull the block downwards but the spring force act upwards, countering effect of gravity, block will attain equilibrium. But there is EPE stored in spring even if the block is hanging at rest as well as GPE since at a height both have same magnitudes but opposite directions. When the block is further pulled downwards, there will be some more EPE (Due to deformation of spring) added to existing EPE caused due to gravity. When you leave the block, using both the EPE given to it by you and by gravity will convert to KE. KE here is maximum not when spring completely reaches its original length, It is maximum at the point where the block remained at rest earlier (Point where Spring force and gravitational force were equal). That KE is again spent to move upwards until the EPE (Caused due to deformation) and GPE will cancel that whole KE at maximum possible upward displacement. Of course, this total EPE added with GPE will again start converting to KE and so on...

Point to be noticed:
• The extra EPE given to spring when you pulled it down at the beginning will be equal to GPE added to EPE when block reaches maximum upward displacement. So work done by you to pull block down will be converted to GPE when reaches upper extreme.
• In fact, this oscillation of block is dealt by only EPE given by you to the block when pulled downwards. The same EPE you gave converts to GPE when it displaces upwards.
• And the EPE caused due to gravity at beginning does nothing since it keeps cancelling out throughout the process.
Now, think of when block is placed on floor with spring attached to rigid support. No gravity consideration and consider floor to be frictionless for easy understanding.
Hope it helps, wrote with maximum detail.

5. Jun 23, 2017

### xJJx

Thank you so much for your replies. I'm talking about a scenario where an ideal spring is fixed at one end and hanging freely from the other end, with NO mass connected to that other end. If an external force is applied to the spring to make it oscillate, and then that force stops acting as soon as it begins to oscillate, would my description above be fully correct? (assuming there's no damping/air resistance etc). Also, I thought every object above the Earth's surface has some GPE, that's why I said the spring does above, was I wrong to say this?
Thank you both for your help! :)

6. Jun 24, 2017

### xJJx

wait sorry I just realised an ideal spring has no GPE since we assume that it's massless

7. Jun 24, 2017

### xJJx

I'm confused at how an ideal spring can have kinetic energy though, since it has no mass.

8. Jun 24, 2017

### Nidum

@xJJx

No mass means no KE , infinite accelerations and zero times for responses to perturbations - which is clearly nonsensical .

You are unfortunately trying to analyse a problem that cannot exist in reality .

9. Jun 24, 2017

### xJJx

I know, I have to learn about the oscillation of a mass-spring system under SHM, with the spring being an ideal one (i.e. a massless, frictionless and linear spring). But I'm trying to figure out if an ideal spring can oscillate without a mass being connected to one end of it. Also, say it can, how would it be possible for a massless object to move if its KE is 0? I know, for example, a photon is massless but can move, I just don't get how. I can imagine real-life scenarios, but not so much theoretical ones like this. I have to learn it for my syllabus though.

10. Jun 26, 2017

### Feodalherren

You already answered your own question. If it's an ideal spring the question you're asking does not make sense. It's like asking "what does blue taste like"? When you're dealing with the spring you're using Newtonian physics in which mass is conserved and energy and mass are not two sides of the same coin. When you're dealing with the photon you're entering the realm of modern physics.