### The Dentzel Carousel In Faust Park

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A few rough measurements indicated that: (1) on the third row, one of the horses moves through about 4 and 1/4 peaks (up-down movements) per single turn, (2) the high to low position of the horse is about 13 inches, (3) the distance from the center of the carousel to the center of this horse's pipe is about 21 feet 3 inches. The speed changes but seems to reach a max of about one turn per 15 seconds.

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We are working with vector valued functions now so we thought we would represent the motion of this horse as

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r(t)= 21.25 cos(t) i + 21.25 sin(t) j + .5417 sin(4.25*t) k

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for a start.

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The horse moves up and down since the pole through the horse is attached to a crankshaft. What changes would you make in the
vector valued function to approximate the horse motion?

Dentzel Carousel Co. http://www.dentzel.com

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William V. Thayer, PedLog