### 2-D Simple Harmonic Motion: F_{x }= -k_{x}x
and F_{y }= -k_{y}y

__NOTES__:

The spring constant ratios are chosen to produce periodic motion: the ratio of
the frequencies must be a rational fraction, and frequency is proportional to k^{2}.

If the 2-D path is derived in terms of the phase difference d
between x and y motion, students can be queried on how to choose the initial
conditions to obtain the desired phase difference:

- d = 0: vx0 = vy0 = 5
- d = p: vx0 = -vy0 =
5
- d = p/2: x0 = vy0 =
5

__Reference__: Jerry B. Marion and Stephen T. Thornton, *Classical
Dynamics of Particles and Systems* (4th edition, 1995) p. 111-114.

* This demonstration was written by Tim Gfroerer and scripted by Mario
Belloni.