## Crankshaft Position Function

Limits, differentiation, related rates, integration, trig integrals, etc.
hangao435
Posts: 1
Joined: Fri Jun 25, 2010 3:01 pm
Contact:

### Crankshaft Position Function

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.

stapel_eliz
Posts: 1738
Joined: Mon Dec 08, 2008 4:22 pm
Contact:
Parametric equations may be viewed as functions of $t$, so you would have functions $x(t)$ and $y(t)$, where $x$ and $y$ are functions of $t$. At a guess, this might be what is intended...?