I'm given some initial conditions for a 2-d isotropic oscillator:(adsbygoogle = window.adsbygoogle || []).push({});

At t=0: x=A, y=4A, dx/dt = 0, dy/dt = 3wA

Solving the differential equations of motion and using those conditions, I get the following:

[tex]let\ \gamma = tan^{-1}(-3/4)[/tex]

[tex]x(t) = A cos(\omega t)[/tex]

[tex]y(t) = 5A cos(\omega t + \gamma)[/tex]

The problem then asks to show that the motion is confined to a box of dimensions 2A and 10A. To me this seems inherent just by looking at the amplitudes of x and y, but maybe I'm missing something?

The book (Fowles & Cassiday, 7th ed) goes into this big long spiel to show the confinement of motion. It rewrites y in terms of x, skips a million trig substitutions, and ends up with an equation of the form:

[tex]ax^2 + bxy + cy^2 + dx +ey = f[/tex]

And it says this can tell you, based on the discriminant, whether it's an ellipse, a parabola, or a hyperbola, and what it's bounds are.

So I took my x and y (listed above), put y in terms of x, did some trig substitutions, rearranged, squared both sides, and ended up with:

[tex]x^2 - 8xy + y^2 = 9[/tex]

Now,how does this help me describe the motion any more than my original equations for x and y? And how does this help me to show that the motion is confined to a box of dimensions 2A and 10A any more than the amplitudes of the original equations do?

Or should I ignore that whole part of the book?(probably not, but you never know)

My position equations seem ok since they agree with the IC's, and http://sporkstorms.org/tmp/2Doscillator.png" seems sane, and is clearly between -A,A and -5A,5A (which is what the problem text suggested).

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: 2D isotropic oscillator

**Physics Forums | Science Articles, Homework Help, Discussion**