Object within a Pan Spring Motion

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AI Thread Summary
The discussion focuses on analyzing the motion of an object within a pan attached to a spring, particularly in the context of simple harmonic motion (SHM). For part a, the combined mass of the system is used to derive the angular frequency and period of oscillation, concluding that the time to return to equilibrium is half a period. Part b presents challenges in determining the forces acting on the egg, including gravitational force and the spring force, while emphasizing the need to consider accelerations during SHM. The maximum acceleration occurs at the extremes of motion, and the discussion highlights the sinusoidal nature of spring motion. Overall, the analysis revolves around understanding the dynamics of the egg's motion in relation to the spring's behavior.
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Homework Statement


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Homework Equations


Spring motion equations
##\omega = \sqrt{\frac{k}{m}}##
##KE = \frac{1}{2}k \Delta x^2##
##F = -k \Delta x##
##T = \frac{1}{f}##
##f = \frac{\omega}{2 \pi}##

The Attempt at a Solution


Part a is straightforward I believe.
Simply combine the masses as m+M, into ##\omega = \sqrt{\frac{k}{m+M}}##
So then ##T = \frac{1}{f} = \frac{2 \pi}{\sqrt{\frac{k}{m+M}}}##
I believe the time it takes to return equilibrium should half a period, so we get ##\frac{\pi}{\sqrt{\frac{k}{m+M}}}##

Part b is the tricky part, I'm not sure how one goes about it. I guess the first step would be identifying all the forces on the egg
The egg has an upwards normal force from the pan, along with a downwards force from gravity.
It would experience a force from the spring when it is being pulled up or down.
I imagine you would try to find the sum of forces and find when it is not in equilibrium?
 

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srekai said:
the time it takes to return equilibrium should half a period
Think that through again.
srekai said:
Part b is the tricky part
Consider accelerations. During SHM, where in the cycle is the maximum acceleration? What determines the maximum acceleration of the egg?
 
haruspex said:
Think that through again.

Consider accelerations. During SHM, where in the cycle is the maximum acceleration? What determines the maximum acceleration of the egg?

Yeah definitely half a period, since you pass by the equilibrium point after half a period. Since spring motion is sinusoidal, it'll start from rest, into maximum amplitude, then passes by the equilibrium point, into the compressed form, back out into the equilibrium point in one period.

Acceleration is greatest at the maximum amplitudes, so either when it's fully stretched or compressed.
##a = -(2 \pi f)^2 x##
 
srekai said:
it'll start from rest, into maximum amplitude, then passes by the equilibrium point, into the compressed form, back out into the equilibrium point in one period.
Right, and the question is asking for the time from one extreme to equilibrium.
srekai said:
Acceleration is greatest at the maximum amplitudes, so either when it's fully stretched or compressed.
Yes. But is there anything in the set-up that limits the acceleration to which the egg can be subjected?
 
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