Question

A diving board oscillates with simple harmonic motion of frequency 3.85 Hz.
What is the maximum amplitude with which the end of the board can vibrate in order that a pebble placed there not lose contact with the board during the oscillation?

Answer 1

The max acceleration of the end of the board is:

    a_max = Aw² = A (2πf)²

The idea is that if this acc exceeds g, then the pebble willlose contact (because the acc of the board will "overcome" the accof g pulling down).

So to find the maximum allowable value of A, we can set thisequal to g:

     g =   A(2πf)²     or     A = g / 4π²f²

or:

A = 9.8 / 4 * π² *3.85² = 0.0167 meter