Can we determine the A's and
'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):
cm,
(so both normal modes are at maximum amplitude at t=0).
The angular frequencies
and
have already been measured (see Table i).
We see that Eq. (3) is much simpler,
and we predict that
![]()
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.