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Equation of oscillating circle

  1. Feb 24, 2014 #1
    http://gyazo.com/bc7f6da4d4c4aca300bb5efb2410fc8d.png


    The problem, and my solution are in the image. I need help on finding the equation of the osculating circle, I found radius but I don't know where to go from there. Also if you could just check if my math seems correct that would help me too, but my main problem is how I find the eqn for the circle... thanks in advance
     
  2. jcsd
  3. Feb 25, 2014 #2

    haruspex

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    You made a mistake differentiating t3.
    You have the radius of curvature; from the tangent you can find the normal vector.
     
  4. Feb 25, 2014 #3
    Yea I noticed the error, I'm working on fixing it now. Can you elaborate more on how to find the radius? I'm not very good at this stuff..
     
  5. Feb 25, 2014 #4

    haruspex

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    You said you had the radius. If so, all you need is a line the circle's centre must lie on. The normal to the curve is that line.
     
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