# Math Help - Heeeeeeelpppp!!!! !

1. ## Heeeeeeelpppp!!!! !

Could a sine or cosine functions describe the motion of a ferris wheel, if the center of the wheel moved up and down during the period?

HELPPPPPPPPP!!!! PLEZ AND THANK U

2. Originally Posted by rocklee1211
Could a sine or cosine functions describe the motion of a ferris wheel, if the center of the wheel moved up and down during the period?

HELPPPPPPPPP!!!! PLEZ AND THANK U
Do you mean could a sine or cosine function describe the motion of a point on a ferris wheel if the center of the wheel moved up and down sinusoidally during the period?

As stated the answer simply cannot be determined. The answer to the one that I am guessing you meant is: not in general.

The height h of a point from the ground on a ferris wheel of radius R and angular speed $\omega$ and center height H can be modeled by
$h(t) = H + R~sin(\omega t + \phi)$

If the height of the center H is now varied sinusoidally, then
$h(t) = A~sin(\omega ' t + \phi ') + R~sin(\omega t + \phi)$
which is the sum of two sinusoidal functions. The only way that this is going to be a sinusoidal function is under the following conditions:
$A = R, \omega ' = \omega, \phi ' = \phi$ (oscillations are perfectly in phase)
or
$A = R, \omega ' = \omega, \phi ' = 2 \pi - \phi$ (oscillations are perfectly out of phase.)

-Dan