Physics Activity - Simple harmonic motion (Oscillations) using string and rubber bands

Link to Simple harmonic motion lesson plan.
Link to Simple harmonic motion training video.

Simple harmonic motion is a type of periodic motion, where there is a restoring force that is directly dependent on the displacement of the system. For example, for something like a spring, the force needed to stretch a typical spring depends on the stretch distance; if you stretch a spring 5 centimeters with some force, then you will need twice the force to stretch and hold a spring 10 centimeters, and three times the force to stretch and hold the spring with a 15 centimeter stretch. This is Hooke's law, where Force = (constant)(stretch distance), or F = kx. The constant k is called the spring constant, and it basically measures how stiff a spring is. This same law generally works for rubber bands, if one does not have springs available.

This experiment is relatively simple to do with rubber bands (to replace springs) and strings (for a pendulum). Teachers and students can make measurements of the periods of both oscillating springs that are bouncing up and down when there are masses hung from the rubber bands and swinging pendulums. There is a separate experiment for figuring out details of a pendulum you may want to do before this experiment. 

The period of a bouncing rubber band as a function of the mass hung on the rubber band gives a square root relationship when graphed. This is identical to the graph for a pendulum of the period as a function of the length of the pendulum, which is also a square root graph. These are shown in the training video. This can show the general behavior of any system that is simple harmonic in it vibrations - they are all the same mathematically. There is a video for advanced students showing the mathematics for an oscillating spring, as well as a video for the mathematics of a swinging pendulum at small angles. The mathematical analysis will be identical for these two examples, which is measured in this experiment.

Have fun with the simple harmonic motion experiment and training video.