A diving board oscillates with simple harmonic motion of frequency 4.6 cycles per second. What is the maximum amplitude with which the end of the board can oscillate in order that a pebble placed there does not lose contact with the board during the oscillation?

Answer 1

acceleratoin= -w^2 y
but the max acceleration cannot be greater than g to keep the pebble in place, so
g=-w^2*Amplitude

w=2PIf=9.2PI
solve for amplitude

Answer 2

.03