Simple Harmonic motion of sand grain

[nokia8650]

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

 

[Doc Al]

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?)

 

[nokia8650]

Im not sure... the acceleration of free fall is surely the maximum acceleration that the sand can have isn't it?

Thanks

 

[Doc Al]

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?

 

[nokia8650]

It will seize to oscillate with SHM?

 

[Doc Al]

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?

 

[nokia8650]

The plate and sand particles would separate?

 

[Doc Al]

Exactly! You'd see the sand particles start to bounce around.

 

[nokia8650]

That makes sense! Thank you so much!