# Does a slinky move up and down equally?

• Bagwan
In summary, the distance the slinky moves down the first time may not be equal to the distance it moves back upwards, as it depends on the initial conditions and what is meant by equal distance. The reference point for this comparison is the equilibrium point of the slinky. It is likely that there will be more than one oscillation mode excited, therefore resulting in unequal distances. However, in a purely theoretical scenario, if the slinky is pulled down from its resting position and then released, it may bounce back up to the same distance. The elasticity and mass of the slinky will also affect the distance it travels. This behavior is only observed after half of the oscillation cycle, not the full cycle.

#### Bagwan

Let's say there is a slinky being held up. If I pull the bottom of the slinky, it will keep oscillating/vibrating/swinging up and down continuously, until it comes to a stop.

My question is, is the distance the slinky moves down the first time EQUAL to the distance it moves back upwards?

Or is one distance larger than the other?

Thank you very much in advance.

This depends on your exact initial conditions and what you mean by equal distance (the center of mass displacement from its equilibrium or perhaps the endpoint position).

The reference point I'm talking about is the equilibrium, sorry I didn't mention that! At first, the slinky would be at its rest position, then pulled slightly to the bottom.

You need to specify exactly how it is pulled (is it pulled down and released from rest, is it just given some momentum, etc).

What do you mean with resprct to the equilibrium? The position of the end? The position of the center of mass of the slinky? Something else?

Regardless of the setup, the answer is likely that it is not going to go up and down equally as you are likely to excite more than one oscillation mode.

Purely theoretically, if I were to allow a hanging slinky to reach its resting position (that is, the location where the slinky doesn't move at all while hanging), and then my hand pulled the bottom of the slinky downwards towards the ground slightly (perhaps 10 centimeters below the resting position), if there were a magical ruler that measured the distance it pushed back upwards from the resting position, would that also be 10 centimeters?

If it wasn't less, it would keep bouncing indefinitely.

Yeah you're right about that, but I was just thinking that they both could be equal, and then in the next oscillation both distances could go down by the same amount. That would still lead it to stopping, right?

Now in the other direction would be a different story, if you lifted the end of the coil 10 cm and let it accelerate towards the ground it might travel further depending on its elasticity versus mass.

jerromyjon said:
If it wasn't less, it would keep bouncing indefinitely.
He isn't asking about more extension after a full cycle, just after half the cycle. Why shouldn't a non-linear spring, go higher above the equilibrium than it was pulled below it?

## 1. What makes a slinky move up and down?

A slinky moves up and down due to the force of gravity acting on it. The gravitational pull causes the slinky to stretch downwards, and then the tension in the coils causes it to bounce back up.

## 2. Does a slinky move up and down equally?

Yes, a slinky moves up and down equally as long as the surface it is resting on is flat, smooth, and level. If the surface is uneven, the slinky may move more in one direction than the other.

## 3. How does the length of a slinky affect its up and down movement?

The length of a slinky affects its up and down movement by changing the frequency and speed of the wave traveling through it. A longer slinky will have a lower frequency and slower speed, while a shorter slinky will have a higher frequency and faster speed.

## 4. Is air resistance a factor in a slinky's up and down movement?

No, air resistance is not a factor in a slinky's up and down movement. The force of gravity and the tension in the coils are the main factors that determine the movement of a slinky.

## 5. Can a slinky move up and down forever?

No, a slinky cannot move up and down forever. The motion of a slinky will eventually slow down and come to a stop due to friction and other external factors. Additionally, the slinky may lose its elasticity over time and will no longer be able to bounce back up as it did before.

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