The co-ordination bag
For my demonstration in Physics 420C I chose to attach an accelerometer to a coordination-bag (also called a double ended bag) in order to show the oscillatory motion. Accelerometers are very practical physics teaching tools. They are cheap and versatile due to their increased use in industrial applications such as airbags. Once you have set up the apparatus, you can use the accelerometer for whatever you like. For increased versatility, you can buy a portable data-logger, or if you are ambitious you can communicate with the sensor wirelessly. I was working with a budget so my set up is cost-effective. The co-ordination bag came from a sports equipment store. The math in this demo is at the first year university level. I presented to a highschool advanced placement class. For the most part they had a good idea of what was going on, and there were many students interested in the process of assembling the apparatus. This demo was designed partly to engage the students with the contemporary lab technology available. Using computers to collect data is an essential part of university level physics and can be an excellent teaching tool. The apparatus here could be applied to a variety of dynamic experiments besides oscillatory motion. The real-time, visual exposure to a mathematical interpretation of the motion helps to bridge the gap between reality and paper. During the class we discussed what we were seeing on the computer projector. I asked the students questions about what the acceleration would look like for a bag with tougher bungies. I asked what would happen to the time-period if we punched the bag harder or softer or if we used a heavier bag. Before answering any of these questions I challenged someone to draw a free-body-diagram on the board. We also discussed the relationship between amplitude and energy and how the frequency of the system is independent, depending on the mass and hooks' constant. Below is a diagram of the displacement of the bag in one dimension.The bottom shows y=Acos(x), where x=wt. The top shows the actual position of the bag at increments of (1/8)T.