This module purports to solve an 'eigenvalue' problem by finding the length of a simple pendulum with a given period. This problem is not typically considered an eigenvalue problem since the eigenvalue, which would be the angular frequency, can be calculated directly from the period. Students are asked to find the eigenvalues, though I suspect most students would assume they are looking for the length of the pendulum (as does the lesson plan), which is not the eigenvalue. In my opinion, this lesson does not illustrate anything useful about eigenvalue problems and would confuse most students.
The Pendulum applet is used to solve the nonlinear equation of motion for a simple pendulum (what is a 'thin rigid pendulum'?). The non-obvious abbreviation 'saa' is used for 'small angle approximation'. This should be spelled out. The autoscale option also is confusing, since it scales all values to the range [-1,1] rather than scaling the y axis. For initial angles of 0.1 rad (I'm assuming this is in radians since there are no units on any quantities) the numerical solutions track the small angle approximation, which is as it should be. Increasing the amplitude of oscillation correctly increases the period, as occurs in the nonlinear regime (where, by the way, the eigenvalue concept is not applicable). The program also works when the pendulum is continuously spinning either clockwise or counterclockwise.
