# Homework Help: Simple Harmonic motion of sand grain

1. Sep 14, 2008

### 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

Last edited: Sep 14, 2008
2. Sep 14, 2008

### Staff: Mentor

I suspect they mean "while keeping the amplitude the same". What happens then? (Hint: What's special about the initial max acceleration?)

3. Sep 14, 2008

### nokia8650

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

Thanks

4. Sep 14, 2008

### Staff: Mentor

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?

5. Sep 14, 2008

### nokia8650

It will seize to oscillate with SHM?

6. Sep 14, 2008

### Staff: Mentor

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?

7. Sep 14, 2008

### nokia8650

The plate and sand particles would seperate?

8. Sep 14, 2008

### Staff: Mentor

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

9. Sep 14, 2008

### nokia8650

That makes sense! Thank you so much!