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Classical mechanics can be summarized as techniques for finding the equations of motion for a system. In the classical mechanics capstone, a unique opportunity presents itself. The first part of the course can be spent reviewing topics students saw in the lower division and paradigms courses: Newton's laws, energy conservation, non-uniform circular motion, oscillations, center of mass, etc. While reviewing, it's possible to kick the level up a notch by considering either complex problems that combine these topics or problems involving systems of particles. The second part of the courses introduces students to new methods for finding equations of motion.

A productive strategy in this course is to use touchstone problems. These are problems that can be solved using several different methods and can be used to explore the differences and advantages of different methods.

Pendulum problems make good touchstone problems for two reasons. First, the large-amplitude-pendulum is a non-trivial problem using all the different classical mechanics methods. Second, because pendulum problems can be spruced up with simple modifications.

• simple harmonic oscillator
• anharmonic oscillator
• accelerating platform pendulum
• spring pendulum
• conical pendulum
• spherical pendulum
• bead on a rotating hoop
• ball rolling on a circular track
• coupled pendula

Another touchstone problem that I've used is the block sliding down the frictionless wedge.