Normal coordinates of a system of equations

I have the system:

\begin{cases} x(t) = 4E\cos{(\omega_{1}t - \phi_{1})} + 2F\cos{(\omega_{2}t - \phi_{2})}\\ y(t) = 5E\cos{(\omega_{1}t - \phi_{1})} - F\cos{(\omega_{2}t - \phi_{2})} \end{cases}

How do I find the normal coordinates of this?

(edited 10 years ago)

I have the system:

\begin{cases} x(t) = 4E\cos{(\omega_{1}t - \phi_{1})} + 2F\cos{(\omega_{2}t - \phi_{2})}\\ y(t) = 5E\cos{(\omega_{1}t - \phi_{1})} - F\cos{(\omega_{2}t - \phi_{2})} \end{cases}

How do I find the normal coordinates of this?

I presume you mean find the cartesian form of the curve.

It's rather nasty.

Do you really need it? Is that the whole question?

Original post by ghostwalker

I presume you mean find the cartesian form of the curve.

It's rather nasty.

Do you really need it? Is that the whole question?

By normal coordinates I meant combinations of

x

and

y

such that one of the two normal modes is excited but I have understood my lecturers material at this point, thanks.

By normal coordinates I meant combinations of

x

and

y

such that one of the two normal modes is excited but I have understood my lecturers material at this point, thanks.

Excellent - always best when you're able to work your own way through to the solution.

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