- #1
Tricky557
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Homework Statement
Find an equation of the oscillating circle to y=ln(x) at the point (1,0)
Homework Equations
p will = the 2nd derivitive of y
u will = the 1st derivitive of y
i will = the 2nd derivitive of x
o will= the 1st derivitive of x
(po - ui)/(|V|^3) = k(curvature)
1/k = r(radius)
x=t
y=ln(t)
V=u ---> I think?
The Attempt at a Solution
o = 1
i = 0
u= 1/t
p= (-1/(2t^2))
I plugged those values into the curvature equation, (po - ui)/(|V|^3) = k
(1/t)/((1+(1/t^2))^(1/2))
The value I got for k was 1. So the radius also = 1. One of the issues I have with this problem is that I'm not sure I plugged in the correct velocity. I know that velocity = the 1st derivitive of the vector(so would it be u?).
So now with the radius, I need to find the tangent unit vector(right?).
T= V/|V|
And this is the point where I get stuck again. I'm really not sure if my value of the velocity is correct or not.
Once I get the Tangent unit vector, I think I'm supposed to add that vector to the point that I"m given, in this case (1,0) in order to find the center of the circle. And with the center, I can get the equation of the circle.
My apologies on the bad notation as far as the equations goes, I don't really know how to type out things like this.