Imagine a rubber beam. One en is fixed and the other is pulled down 5cm and released. The beam wobbles until it comes to rest.
Independent (what I change): length of rubber beam
Dependent (what I measure): time to come to rest
Controlled (what stays the same): everything else
I got a relationship of T=kL^2
The question is why this relationship. I can´t seem t find the answer
The Attempt at a Solution
One of the observations was that the shorter the beam, the faster it moved. When given potential energy (when ppulled down), then released, part of it gos to KE and the rest to termal (energy loss). If it moves faster, it looses energy faster so the time to come to rest should be less. This explains why it increases with length but not the x-squared relationship.
On the internet I have see things about stiffness, an iron beam, to support the same weight has to have a stiffness of the squared of the length. but does stiffness affect the time to come to rest?
This might also go into SHM, but I'm not sure