Spring-Block system executing SHM in a freely falling elevator

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Homework Help Overview

The discussion revolves around a spring-block system in a freely falling elevator, exploring the conditions under which the block executes simple harmonic motion (SHM). The original poster presents a scenario where a block of mass m is suspended from a spring in a stationary elevator, which then begins to fall after the cable breaks. The goal is to demonstrate that the block executes SHM with a specific amplitude.

Discussion Character

  • Exploratory, Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants discuss the application of pseudo forces and the implications of the elevator's free fall on the spring's behavior. There are attempts to derive equations of motion for both the block and the spring's attachment point. Questions arise about the nature of forces acting on the block and the ceiling of the elevator, as well as the assumptions regarding the mass of the elevator relative to the block.

Discussion Status

The discussion is active, with participants exploring various interpretations of the problem. Some suggest ignoring certain forces or simplifying the system, while others question the validity of these assumptions. There is no explicit consensus, but multiple lines of reasoning are being examined, indicating a productive exploration of the topic.

Contextual Notes

Participants note the complexity of the system, particularly regarding the mass of the elevator and the effects of free fall on the spring's forces. There is an ongoing debate about the assumptions that can be made, particularly concerning the acceleration of the block and the nature of the restoring force in the context of SHM.

  • #31
If ##\frac{\mathrm{d} ^{2}x_{\text{eq}}}{\mathrm{d} t^{2}} = g## then what is ##x_{\text{eq}}(t)## if the initial height of ##x_{\text{eq}}## above the ground was some value ##d## and it started off at rest before going into free fall?
 
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  • #32
WannabeNewton said:
If ##\frac{\mathrm{d} ^{2}x_{\text{eq}}}{\mathrm{d} t^{2}} = g## then what is ##x_{\text{eq}}(t)## if the initial height of ##x_{\text{eq}}## above the ground was some value ##d## and it started off at rest before going into free fall?

Then xequili(t)=g.(t^2)/2 + d
 
  • #33
vijaypandey93 said:
Then xequili(t)=g.(t^2)/2 + d
Right so plugging back into Newton's 2nd law we have ##m\ddot{x} = -kx + mg + k(\frac{1}{2}gt^{2} + d)## in the ground frame. Is this the equation for simple harmonic motion? If you solve this will you get an ##x(t)## that is purely sinusoidal?
 
  • #34
WannabeNewton said:
Right so plugging back into Newton's 2nd law we have ##m\ddot{x} = -kx + mg + k(\frac{1}{2}gt^{2} + d)## in the ground frame. Is this the equation for simple harmonic motion? If you solve this will you get an ##x(t)## that is purely sinusoidal?

we can't say that necessarily because simple harmonic motion is caused by a force which has a restoring effect and opposite to the displacement.so all the terms may get added and may give a positive value which is ofcourse not the hall mark of SHM.
 
  • #35
WannabeNewton said:
Right so plugging back into Newton's 2nd law we have ##m\ddot{x} = -kx + mg + k(\frac{1}{2}gt^{2} + d)## in the ground frame. Is this the equation for simple harmonic motion? If you solve this will you get an ##x(t)## that is purely sinusoidal?


okay i'll solve and then check it.thanks a lot
 
  • #36
You don't have to explicitly solve it if you don't want to; you can tell just by looking at the equation.
 

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