# Horizontal and vertical oscillations of a loaded spring

1. Sep 25, 2011

### logearav

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

Revered Members,
I have attached two images which explain horizontal and vertical oscillations of a loaded spring. In horizontal oscillations the restoring force is taken as F = -kx.
But in vertical oscillations the restoring force is taken as F = kdl.

2. Relevant equations

3. The attempt at a solution
Restoring force is opposite to the direction of displacement so negative sign is included. But why in vertical oscillations the restoring force is
F = kdl. Why not F = -kdl?
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

#### Attached Files:

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• ###### vertical oscillations.png
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2. Sep 25, 2011

### CheckMate

Because gravitational force is negative ?

Sign is really arbitrary. Mg can be positive or negative. If it is negative than restoring force is positive and vice versa.

3. Sep 25, 2011

### logearav

Thanks for the reply CheckMate. But i can't understand.

4. Sep 25, 2011

### CheckMate

Think about the force as a vector, the sign just states the direction of the vectors in a x,y plane.

Up can be associated to positive and down negative, that is why it is F=kdl rather than F=-kdl . It is because up was chosen as positive and F = -mg.

In the first page, left is negative and right is positive. That is why the horizontal force is negative. But it really doesn't matter, as long as the opposite force has an opposite sign.

Last edited: Sep 25, 2011
5. Sep 25, 2011

### logearav

The spring comes down vertically from its initial position, that is an increase in length dl was observed. Now the role of restoring force is to bring the spring back to its original or initial position, so it should be -kdl. This is where my doubt arises?

6. Sep 25, 2011

### CheckMate

Force tells us : how much acceleration is done on an object of mass m and where is this acceleration direction.

There is an increase in L, but the acceleration is toward down. The mass of the spring isn't changing, the mass of the block isn't changing but the position of the block is. And making it go down is seen as negative force.

7. Sep 25, 2011

### CheckMate

Lenght of a spring doesn't matter. It's the position of the mass attached to the spring that matters.

In this case, the position is changing downwards (which is seen as negative), than to bring it up you need to increase it's position.

Imagine the block is at 5 meters up from the ground.

It goes to 2m from the ground (the position has decreased by 3 meters relative to the ground)

When it goes back up the position increases by 3.

8. Sep 27, 2011

### logearav

Thanks for the reply Checkmate. I could understand this but i could not understand the following post

9. Sep 27, 2011

### logearav

Lenght of a spring doesn't matter. It's the position of the mass attached to the spring that matters.

I can't understand the quoted lines