2-D Simple Harmonic Motion: Fx = -kxx and Fy = -kyy

Spring constant ratio:

1:1

1: 4

1: 9

User Defined Controls:

x0 =   

 vx0 =   

y0 = 

vy0 =   

kx = 

ky =   

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 k2.

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:

  1. d = 0: vx0 = vy0 = 5
  2. d = p: vx0 = -vy0 = 5
  3. 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.