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Simple Model

Can we determine the A's and tex2html_wrap_inline451's used in Eq. (3) that apply in Fig. 4? This is generally a daunting task, for the parameter space to explore is very large.

Our initial conditions (glider 1 displaced -7.5cm, glider 2 displaced 0.0, both released from rest) make this easy. As shown in the bottom panel of Fig. 2, adding the two normal modes, both at equal maximum amplitude A, displaces glider 1 by 2A and leaves glider 2 at equilibrium, with both gliders at rest.

We can now identify the four constants in Eq. (3): tex2html_wrap_inline493cm, tex2html_wrap_inline495 (so both normal modes are at maximum amplitude at t=0). The angular frequencies tex2html_wrap_inline499 and tex2html_wrap_inline501 have already been measured (see Table i). We see that Eq. (3) is much simpler, and we predict that
 equation62

In Fig. 5 we see the experimental data and Eq. (4) plotted together. Clearly the agreement is excellent, aside from a small decrease in amplitude due to air drag.



Norris Preyer
Fri Sep 19 10:33:22 PDT 1997