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?

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- May 8th 2008, 05:04 PM #1

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- May 8th 2008, 07:13 PM #2
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 $\displaystyle \omega$ and center height H can be modeled by

$\displaystyle h(t) = H + R~sin(\omega t + \phi)$

If the height of the center H is now varied sinusoidally, then

$\displaystyle h(t) = A~sin(\omega ' t + \phi ') + R~sin(\omega t + \phi)$

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:

$\displaystyle A = R, \omega ' = \omega, \phi ' = \phi$ (oscillations are perfectly in phase)

or

$\displaystyle A = R, \omega ' = \omega, \phi ' = 2 \pi - \phi$ (oscillations are perfectly out of phase.)

-Dan