Coupled pendula with measure Dynamics

Principle

Two identical gravity pendula with a particular characteristic frequency are coupled via a "soft" spiral spring. The amplitudes of both pendula are recorded as a function of time. The coupling factors are determined by way of different methods. Then, the local
points of the oscillation are integrated into the video.

Benefits

• Large and sturdy set-up suitable for demonstration and lab courses as well
• Live data-logging system to measure the oscillations of both pendula at once
• Easy measurement and evaluation via movement tracking software

Tasks

1. Determination of the spring constant of the coupling spring. 
2. Determination and adjustment of the characteristic frequency of the uncoupled pendulum. Determination of the moment of inertia of the pendulum.
3. Graphical representation of the oscillation of the two pendula as a function of time and determination of the oscillation frequency compared to the theoretical oscillation frequency for
   A)   the "in phase" oscillation.
   B)   the "antiphase" oscillation.
   C)   the beat case.

Learning objectives

• Spiral spring
• Gravity pendulum
• Spring constant
• Torsional vibration
• Torque
• Beat
• Angular velocity
• Angular acceleration
• Characteristic frequency