What Determines the Amplitude of a Vibrating Membrane?

[furtivefelon]

hi, this is the last question I'm having trouble with.. the question is:

Fine sand is sprinkled on the horizontal membrane, which vibrates in the vertical direction with frequency f = 500 Hz. The sand particulates bounce at the height of 3 mm over the level of the position of equilibrium of the membrane.
What is the amplitude of the membrane’s vibration?

I imagine that as each sand particulates hits the membrane, the membrane would vibrate for several seconds, and it would be much lower in amplitude than the height sand bounces.. However, I don't have a clue currently how to go about finding that specific amplitude.. Can someone give me a clue as where to begin?

Thank you very much

 

[member 553083]

The amplitude of the membrane's vibration can be calculated using the equation: A = (h/2)*(f/f_0)^2, where h is the height of the sand particulates bouncing over the level of the position of equilibrium, f is the frequency of the vibration, and f_0 is the resonant frequency of the membrane. Therefore, the amplitude of the membrane's vibration would be A = (3mm/2)*(500Hz/f_0)^2.