- #1
Saladsamurai
- 3,020
- 7
Okay then
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
Homework Statement
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