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Calculus/Arc Length of Sine Curve

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Expert: - 6/16/2008


Question
A particle moves at a constant speed of v m/s along a sinusoidal path. The path is described as
y = a*sin(bx)
I want to find expressions for the x and y coordinates as a function of time (t).
Given that at t=0, x=0, y=0.

Answer
To find the arc length of a curve, the equation must be solved from 0 to a using the integral (0 to a)(1+(f'(x))^2)^0.5.

You can see an example in http://www.math.hmc.edu/calculus/tutorials/arc_length/ .

f(x)=a*sin(bx), f'(x)=ab*cos(bx), so (f'(x))^2=(ab)^2*cos^2(bx).
Add 1 and take the entire equation to the 1/2 to get what to integrate.

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