[DEMONSTRATION] - Resonance: Torsional Oscillator and Barton’s Pendulum

From Dr. Denardo, "I forgot to state something at 13:04 minutes. The drive is SLOWLY increased so that the RESPONSE IS IN THE STEADY STATE; otherwise, transients are introduced."
Driven damped torsional oscillator: In the steady state, the maximum response of a driven oscillator occurs on resonance, where the drive frequency equals the natural frequency. The velocity is in-phase with the force, which corresponds to maximum energy transfer, and the displacement lags the force by 90 degrees. For drive frequencies that are significantly less than the resonance frequency, the motion is relatively small, and the displacement is in-phase with the force (quasistatic Hooke’s law). For drive frequencies that are significantly greater than the resonance frequency, the motion is also relatively small, and the displacement is 180o out-of-phase with the force. Sonar projectors are usually driven on resonance to obtain the greatest amplitude.
Barton’s pendulums: Flexible pendulums of different lengths and thus resonance frequencies are driven by a much heavier pendulum. The pendulum with the greatest amplitude has the same length as the driving pendulum, which is due to resonance. The shortest pendulum is nearly in-phase with the driving pendulum, while the longest pendulum is nearly 180o out-of-phase. The results are the same as the driven damped torsional oscillator, but the perspective is reversed here: Instead of the drive frequency being altered, the drive frequency is fixed and the oscillator is changed!