The discussion centers on a Simple Harmonic Motion (SHM) problem involving a mass m falling into a cage with mass M, where the oscillation frequency is determined by the formula √[k/(m + M)]. Participants analyze the conservation of momentum during the collision and the implications for the amplitude of oscillation. The correct amplitude is derived as A = √[k/(M + m)] * m√(2gh)/(M + m), but participants identify errors in their calculations and assumptions about the system's equilibrium. Ultimately, the consensus is that the problem's wording may lead to confusion regarding the initial conditions and the mean position of oscillation.
PREREQUISITESStudents and educators in physics, particularly those focusing on mechanics and oscillatory motion, as well as anyone solving complex SHM problems involving multiple masses and energy conservation.
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: