Analyzing the Motion of Coupled Oscillators Using the WiiMotion Plus Romulo Ochoa, Cris R. Ochoa, and Michael Erickson Department of Physics, The College of New Jersey, Ewing, NJ Introduction The Wii console utilizes a very powerful controller for game-playing. The Wii Motion Plus was introduced in May of In addition to the accelerometers and Bluetooth interface found in regular Wiimotes, it contains gyroscopes that measure the rate of rotation along 3-axes, X (pitch), Y (roll), and Z (yaw), up to ±2,000°/s. Open source code, such as GlovePie ( ),allows PCs with Bluetooth capability to detect the information sent out by the controller. Up to three Wiimotes are used simultaneously to measure the motion of a playground swing, a compound pendulum and of coupled pendulums. Results of our experiments compare well with those predicted by Newtonian mechanics. Experimental Methods Pendulum and playground swing A wooden support was built to hold the Wiimote safely in place. The setup was fastened to a pulley so it could swing freely on a vertical plane. Angular velocity data were collected for small angles. A Wiimote was fastened to one of us (CO), at waist level, while on a playground swing and data was collected under various initial conditions. The simplest experiment was releasing the swing at small initial angles and comparing the measurements with those obtained from simple pendulum calculations. Coupled pendulum motion Two pendulums supports were coupled using a weak spring (k = 3 N/m) as shown in Figure 1. The two Wiimotes reported the angular velocities of their corresponding pendulum. The studies were extended to three pendulums coupled by two soft springs. Abstract The WiiMotion Plus has a dual-axis tuning fork gyroscope and a single-axis gyroscope in addition to three accelerometers. The gyroscopes can measure rotational velocities up to 2000 degrees/s. We present experiments that use the gyroscopes capabilities to follow the motion of a single pendulum, a playground swing, and of coupled pendulums. Figure 2. Plots of playground swing motion. The solid line represents the angular velocity and the dashed line the angular position, both as function of time. Notice the 90 o phase difference between the two data sets. Figure 3. Angular velocities of two coupled pendulums demonstrate motion replicates beats. Figure 4. Graph shows two coupled pendulum motion. The pendulum are moving at 180 degrees out of phase with a slight exchange of energy. Figure 1. Wii controllers in wooden supports as set up for coupled oscillator motion. Figure 5. Motion of three coupled pendulum with random initial conditions. Conclusions The experiments demonstrate that the gyroscopes in the Wii MotionPlus are tools that can be very powerful in physics experiments. The Bluetooth communications gives users freedom to design multiple experiments both in the lab and equivalent experiences in a playground environment. References S. Van Hook, A. Lark, J. Hodges, E. Celebrezze, and L. Channels, “Playground Physics Determining the Moment of Inertia of a Merry- Go-Round,” Phys. Teach. 45, (2007). R. Taylor, D. Hutson, W. Krawiec, J. Ebert, and R. Rubinstein, “Computer physics on the playground,” Phys. Teach. 33, 332–337 (1995). R. Ochoa, F. G. Rooney, and W. J. Somers, “Using the Wiimote in Introductory Physics Experiments,” Phys. Teach. 49, (2011) and references therein. A.Kawam and M. Kouh, “Wiimote Experiments: 3-D Inclined Plane Problem for Reinforcing the Vector Concept,” Phys. Teach. 49, 508 (2011). M. Erickson, C. R. Ochoa, and R. Ochoa, “The Wiimote in the Playground,” Phys. Teach. Accepted for publication AAPT Winter Meeting New Orleans, LA, January 5 -9, 2013