# In an oscillating system (SHM) with a constantly increasing amplitude, how do you relate the constant period with the highest amplitude

For example, I am working on this problem, and I don't know where to begin. All the relationships that I can think of include a constant amplitude. [A (w/w^2) sin/cos theta]

Here's the problem: A person rides on a mechanical bucking horse that oscillates up and down with simple harmonic motion. The period of the bucking is 0.74 s, and the amplitude is slowly increasing. What is the amplitude the rider must hang on to prevent separating from the mechanical horse?

Note: You don't have to give me the answer, just explain the appropriate relationships.

• Compute $y''$, find its maximum value, set equal to gravitational acceleration $g$, and solve for $A$. – DumpsterDoofus Dec 8 '13 at 14:48
• But the mechanical horse doesn't function due to the gravitational force, does it? – user32134 Dec 8 '13 at 17:17
• Correct. But that's not really relevant; the point is to find the amplitude at which there exists a portion of the sine curve where the horse is accelerating downwards faster than what gravity alone would provide to its rider. At that point, the horse and rider will separate. – DumpsterDoofus Dec 8 '13 at 23:53