Diving board oscillates with simple harmonic motion

[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?

 

[wais]

The maximum amplitude with which the end of the diving board can vibrate in order for a pebble placed there to not lose contact would be 0.278 meters. This can be determined by using the formula for simple harmonic motion, A = x0, where A is the amplitude and x0 is the maximum displacement. The frequency of 3.6 cycles per second can also be converted to angular frequency, ω = 2πf, which would be approximately 22.62 radians per second. Using the equation x0 = A cos(ωt), we can plug in the values of 3.6 cycles per second for f, and 22.62 radians per second for ω, and solve for A. This results in an amplitude of 0.278 meters, which is the maximum displacement that the diving board can vibrate without the pebble losing contact.