Free rotational oscillations  recording with CASSY.

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The computer-assisted CASSY measured-value recording system is ideal for recording and evaluating the oscillations of the torsion pendulum. The numerous evaluation options enable a comprehensive comparison between theory and experiment. Thus, for example, the recorded data can be displayed as pathtime, velocity-time and acceleration-time diagrams or as a phase diagram (path-velocity diagram). The aim of the first experiment is to investigate free harmonic rotational oscillations of the general type f(t) = (f(0) · cosvt + G (0) · sinvt) · e-ut where v = ßv 2 0 – u2 v0 : characteristic frequency of torsion pendulum This experiment investigates the relationship between the initial deflection f(0) and the initial velocity v(0). In addition, the damping constant u is varied in order to find the current l0 which corresponds to the aperiodic limiting case. To investigate the transition between forced harmonic and chaotic oscillations, the linear restoring moment acting on the torsion pendulum is deliberately altered in the second experiment by attaching an additional weight to the pendulum. The restoring moment now corresponds to a potential with two minima, i.e. two equilibrium positions. When the pendulum is excited at a constant frequency, it can oscillate around the left minimum, the right minimum or back and forth between the two minima. At certain frequencies, it is not possible to predict when the pendulum will change from one minimum to another. The torsion pendulum is then oscillating in a chaotic manner.

The aim of the experiment P1.5.3.3 is to investigate free harmonic rotational oscillations of the general type