The problem involves a compound system oscillating in simple harmonic motion (SHM) with a mass m falling into a cage of mass M. Participants are discussing the natural frequency of the system and the implications of momentum conservation during the collision between the falling mass and the cage.
There is ongoing exploration of the problem with various interpretations being considered. Some participants have offered insights regarding the assumptions made about the system's equilibrium and the initial conditions. However, no consensus has been reached regarding the correct approach or answer.
Participants note that the problem may lack sufficient information to definitively solve it. There are discussions about the initial conditions of the system and how they affect the calculations, particularly regarding the mean position and the dynamics of the falling mass.
which I believe I didTSny said:
For the frequency, yes, but whether you can ignore it for amplitude depends on initial conditions. Often, the initial condition is a known displacement from equilibrium, and in that case the amplitude will be that displacement. But here, we know the velocity at eq.pos. As it descends, the spring has to take up both that KE and some extra lost PE. So the stronger the gravity the greater the amplitude.
Yes, but what was that in response to?ehild said:
haruspex said:
something like (gm/k) sqrt[1+2hk/(g(M+m))]. But your equation in post #27 does not look correct. It's horrid alright, but I can't find a flaw. Do you see one?ehild said:
haruspex said:
No, I had that wrong. Thanks!ehild said:
SammyS said: