It is worth pointing out that we are still focusing on our two fundamental problems in introductory physics when we work with simple harmonic motion.  We used Newton’s second law to solve for the acceleration acting on a simple harmonic oscillator.  Unlike many of the problems we have previously solved this semester, the acceleration of a simple harmonic oscillator was not constant.  We were able to determine the solution to our Newton’s second law equation, giving us the equations of motion for a simple harmonic oscillator.  Because the set up is the same, regardless of the spring and mass you use, we only needed to solve the problem once to determine how the forces act to change the motion of the oscillator.  This makes it harder to see that we are still working with Newton’s second law, because we are able to jump to the solution for describing simple harmonic motion.

Of course, we can also use conservation of energy with simple harmonic oscillators.  After all the layers we have spent adding to conservation of energy problems this semester, the biggest difficulty for students is often in recognizing how simple conservation of energy tends to be with simple harmonic motion.  For each oscillator, there are only two forms of energy, one kinetic energy and one potential energy, that we need to use.  For a spring and mass system, we need the translational kinetic energy of the mass and the elastic potential energy of the spring.  For a simple pendulum, it is often easiest to use the translational kinetic energy of the mass and its gravitational potential energy.  For a physical pendulum, the energy is being converted between rotational kinetic energy of the extended object and the gravitational potential energy of its center of mass.  Again, the issue is not that we aren’t using conservation of energy, but that we typically don’t have to start at the beginning when we set up a conservation of energy problem for a simple harmonic oscillator.