Simple Harmonic motion of sand grain

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Homework Help Overview

The discussion revolves around the behavior of sand grains on a vibrating plate undergoing simple harmonic motion (SHM). The plate vibrates with a specified amplitude and frequency, and participants explore the implications of increasing the frequency while considering the effects of gravitational acceleration.

Discussion Character

  • Exploratory, Assumption checking, Conceptual clarification

Approaches and Questions Raised

  • Participants discuss the relationship between frequency, amplitude, and acceleration in SHM. Questions arise regarding the effects of increasing frequency on the sand grains, particularly in relation to gravitational acceleration and the conditions under which the grains may lose contact with the plate.

Discussion Status

There is an ongoing exploration of the concepts involved, with some participants questioning the assumptions about maximum acceleration and its relationship to gravitational acceleration. Guidance has been offered regarding the implications of exceeding gravitational acceleration, leading to further inquiry about the behavior of the sand grains.

Contextual Notes

Participants are considering the scenario where the amplitude remains constant while the frequency changes, and they are examining the implications of this setup on the motion of the sand grains.

nokia8650
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Sand grains rest on a horzontal plate. The plate vibrates in the vertical plane with SHM of amplitude 1.5mm at a fixed frequency with acceleration equal to free fall (9.8ms^-2).

What will happen to the grains of sand when the frequency of vibration is increased?

I am unsure of how to tackle this problem. Will the amplitude of oscillation decrease? My working is below:

max acceleration = amplitude*((2*pi*f)^2)If f increases, with max acceleration the same, the amplitude decreases. Is this reasoning and answer correct?

Thanks
 
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nokia8650 said:
What will happen to the grains of sand when the frequency of vibration is increased?
I suspect they mean "while keeping the amplitude the same". What happens then? (Hint: What's special about the initial max acceleration?)
 
Im not sure... the acceleration of free fall is surely the maximum acceleration that the sand can have isn't it?

Thanks
 
nokia8650 said:
the acceleration of free fall is surely the maximum acceleration that the sand can have isn't it?
On the way down it is. And that's the key. What happens if the acceleration of the plate exceeds the acceleration due to gravity?
 
It will seize to oscillate with SHM?
 
nokia8650 said:
It will seize to oscillate with SHM?
Actually, yes. But they're looking for something much more basic (I presume). If you were watching the sand/plate vibrate, you'd immediately notice when the acceleration exceeded g. Why?
 
The plate and sand particles would separate?
 
Exactly! You'd see the sand particles start to bounce around.
 
That makes sense! Thank you so much!
 

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