Shm

[physicsss]

A diving board oscillates with simple harmonic motion of frequency 3.6 cycles per second. What is the maximum amplitude with which the end of the board can vibrate in order that a pebble placed there will not lose contact with the board during the oscillation?

[ceptimus]

The maximum acceleration in simple harmonic motion occurs at the greatest displacement. Do you know the formula that links acceleration, displacement and frequency?

The acceleration due to gravity is g (normally taken as 9.81 m s^-2) and as long as that is greater than or equal to the simple harmonic motion acceleration the pebble will stay in contact.

So you just have to solve:

formula for acceleration at displacement d, at 3.6 cycles/sec = 9.81

Actually it probably would slide off the board before you reached the maximum displacement, but I think it's safe to assume that's what they want you to calculate.

You know how Amplitude is connected to maximum displacement don't you?