Crankshaft Position Function

Limits, differentiation, related rates, integration, trig integrals, etc.
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Joined: Fri Jun 25, 2010 3:01 pm

Crankshaft Position Function

Postby hangao435 » Fri Jun 25, 2010 3:19 pm

As the first part of a related rate problem, I am asked to find equations for the position of the tip of a crankshaft with length 2in and center of rotation at the origin. The crankshaft makes 2 complete rotations per second. The equation needs to be represented in t seconds.
I know that the equation of a circle is x^2+y^2=r^2, but I cannot use this because I have no way to relate time to those values. If I substitute cosine for x and sine for y, I just get a straight line, because that will always equal a constant.
I know that parametric equations would work,but I think I am supposed to find "functions"; although, the book does state "find equations" so, I suppose parametric equations are not forbidden.
I cannot think of any other way to represent the periodic nature of the position of the tip of the crankshaft.

Is there a way to represent the position with a normal function, or must parametric functions be used?

I would ask a professor or teacher, but I am reviewing on my own before I start college, so I don't have access to such resources right now.

Finally, this is part of a Calculus question, but it is initimately related to Trigonometry as well. I am not sure where I should post this. If it should be moved, please let me know. Thank you.

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Postby stapel_eliz » Fri Jun 25, 2010 8:15 pm

Parametric equations may be viewed as functions of , so you would have functions and , where and are functions of . At a guess, this might be what is intended...?

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