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Show that he object moves on an elliptical path

  1. Nov 21, 2009 #1
    Okay then :smile:

    1. The problem statement, all variables and given/known data

    An object moves in the xy-plane such that its position vector is

    [tex]\bold{r} = \bold{i}a\cos(\omega t)+\bold{j}b\sin(\omega t) \qquad (1)[/tex]

    where a,b, and [itex]\omega[/itex] are constants.

    Show that the object moves on the elliptical path

    [tex](\frac{x}{a})^2+(\frac{y}{b})^2 =1 \qquad (2)[/tex]


    I have never studied ellipses, so I am 'googling' them now as we speak. I can see that (2) resembles the equation of a circle except that it includes a couple of scaling factors 'a' and 'b'.

    I am just not sure how to relate (1) and (2) to each other.

    Can I get a friendly 'nudge' here?

    Thanks!

    ~Casey
     
  2. jcsd
  3. Nov 21, 2009 #2
    [tex]\bold{r} = \bold{i}a\cos(\omega t)+\bold{j}b\sin(\omega t) = \bold{i}x +\bold{j}y[/tex]

    Right?

    So [tex]x = a\cos(\omega t), y = b\sin(\omega t) [/tex]

    Just plug it in to the equation (2) in order for it to hold it must hold for all t.
     
  4. Nov 21, 2009 #3
    Right. I thought I was making it more difficult than it is. I don't know why I thought that there was something more to it. Thanks again! :smile:
     
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