I NEED HELP GENIUSES - Physics

[Caz 915]

So in our physics assignment we have to discuss the formula of dynamic SHM. We did some measurements with a spring and some masses and compared our results to this formula:

We then have to discuss the formula's limitations when applied to a 'baby bouncer'. I've said examples like the material of the spring will be different, the baby will input it's own energy into the system (breaking SHM) and that the mass of the baby is much greater than the mass of my sample masses.

I need more examples of limitations of this formula when applied to a baby bouncer.

HELP ME, I know there are some geniuses on this forum.

[Alexandre 2]

Trying to add something to what yo have already, altough it might not be appliable and maybe you know this already.
Well, elasticity behaves, I've been taught, in two different ways. Usually it behaves regularly, when the spring does not get too far from the equilibrium point and it regains its original form. This string elongation zone is called (proportionally) elastic zone (of the graph). When its elongation is too high, its behavior is discribed by the inelastic region (of the graph) and it might suffer deformation. When the elastic region is considered, the following equation applies: F(string)=-K*x, being K the constant of elasticity and x the displacement in the stretching direction (is this how you say it in english?). This is know as Hooke's Law.
Since that equation is deducted from Hooke's law (it needs to be a linear diferencial 2nd degree homegenous equation and the harmonic oscilation fits that role and defines that movement equation) it only works in the elastic zone.

Apart from that, a lot of energy is absorbed by the floor the baby jumps on and by himself since is not rigid but a really deformable body. If he's moving in any direction, then weight distribuition plays a role in movement and in irregular oscilation period throught out the bouncer.

Then there's this really really funny situation in which the baby would make the baby jumper vibrate at its natural frequency (defined as the frequency it would vibrate at if it had only a single momentaneous force input) which would make it jump really really high and which would be incredibly dangerous and hilarious. But this is not very probable

Graphic for elastic region and inelastic region

[Caz 915]

Thank you so much man, this is just what I needed.

[Alexandre 2]

Glad I could help! Good luck

[laggless01 51]

Oh, and there is all the dissipating heat, like friction (air) and an "incomplete" conversion of energy* (which translates to the heating up of the spring, which cools back down due to the air around it). If you're in high school, the latter won't be considered (it's more physics/physical chemistry). They both cause a transfer of energy from the system to the surroundings, so no conservation of energy in your system.



(*basically: Epot -> Ekin + Q in this situation. Q stands for heat)

[Maelstrom 312]

does that actually take gravity into effect? which is constantly going in only one direction, constantly changing the distance and time of oscillation.

As you said, the baby doesn't input energy in a regular rhythm or direction... *looks at Alexander's post* um, yeah, all that stuff.

Also, are there any restrictions on the bouncer to keep the baby from bouncing so much that it could potentially cause injury?