Air Track - Reduced Mass
To demonstrate the change in frequency for two-body oscillations.
Air track with coupled gliders with manual timer, as photographed.
Two gliders are connected by a steel spring as shown in the photograph. With one mass taped down, the other mass vibrates with the standard period for simple harmonic motion: T = 2 pi sqrt (m/k), where k is the spring constant and m is the mass of the vibrating glider. If the two masses are pulled apart and released simultaneously, they vibrate out of phase with each other about the center of mass with a period T = 2 pi sqrt (u/k), where u = Mm/(M+m) is the reduced mass of the system. For M=m the reduced mass u = m/2, and the period is less by a factor of sqrt(2) = 1.414 than in the case of on