Question

Write a function that describes this situation (pics coming...)
Two circles, radius 1, are drawn so their centers are 3 in. apart. Points marked on the circles rotate at a speed of 1 rotation every 4 seconds. Find a function that describes the distance (d) between the two marked points at any time (t).

Answer 1

I know it will be periodic, and can calculate for integral values of t (0,1,2,3,4,etc) but can't figure out how to find when t isn't a whole number.

Answer 2

@ParthKohli @agentx5 can you help?

Answer 3

Gear ratios? I still trying to understand this question the way it's worded, but if that's the case it's just a matter of the ratios of the radii, like you would for pulleys or gears.

Answer 4

Ah wait cycloids...

Answer 5

no, both are rotating clockwise.

Answer 6

http://www.daviddarling.info/images/cycloid.gif (prolate, nested function)

Answer 7

Which of course is going to make it look a whole lot like a sine function

Answer 8

yeah, but a cycloid only describes 1 point. I'm looking for distance between the 2 points.

Answer 9

I know that, which is why it'll end up being two of those together making it a sine function when I think about it visually.

If they were touching it would be double amplitude and half period.

Answer 10

The tricky part is that they start out with an initial distance that also changes with respect to time

Answer 11

Or does it... Hmm, might just be additive.

Answer 12

this is what i've figured out:
\[d(0)= 1\]\[d(1) = \sqrt{13}\]\[d(2) = 5\]\[d(3)= \sqrt{13}\]