Does a slinky move up and down equally?

[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.

 

[Orodruin]

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).

 

[Bagwan]

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.

 

[Orodruin]

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.

 

[Bagwan]

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?

 

[jerromyjon]

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

 

[Bagwan]

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?

 

[jerromyjon]

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.

 

[A.T.]

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?