3a60.00 Hand Held Mass on a String

PURPOSE: To demonstrate the concept of resonance and the idea of phase shift at resonance.

DESCRIPTION: A mass on a string has a natural frequency when it is not driven that is demonstrated by simply
holding one end of the string stationary and allowing the mass to oscillate freely.   To demonstrate driven resonance do the following:

1. With the mass starting at rest, move your hand very slowly side to side to drive the pendulum below the natural frequency. The mass follows the motion of your hand, showing that the mass and the driving force stay 0 degrees apart, exactly in phase for driving frequencies far below the natural frequency of the oscillator.  Very large amplitude oscillations of your hand will have little effect on increasing the amplitude of the pendulum oscillations.

2. With the mass starting at rest, move your hand very rapidly side to side to drive the pendulum above the natural frequency.  The mass moves opposite to the motion of your hand, showing that the mass and the driving force stay 180 degrees out of phase for driving frequencies far above the natural frequency of the oscillator.   Large amplitude oscillations of your hand have very little effect on the amplitude of the pendulum oscillation.

3.  Starting again from rest, move your hand side to side at the natural frequency of oscillation as best that you can.   The phase relationship for resonance is that motion of the your hand is 90 degrees ahead of the motion of the oscillator.  When you synch your hand closely to the natural frquency of the pendulum then a small, tiny motion of your hand, a motion so small that it almost seems imperceptible will at resonance force the mass into oscillation with a very large, wild amplitude.

EQUIPMENT:  as photographed.

SETUP NOTES: none