Hand held mass and spring

PURPOSE: To demonstrate resonance and phase shift at resonance.

DESCRIPTION: The mass on the spring has a natural frequency. Demonstrate resonance as
follows:

Hold the spring with the mass hanging at rest.  Displace the mass and let it oscillate naturally without moving your hand.  Carefully observe the natural frequency and the damping, with no sustained oscillation.

With the mass hanging at rest, move your hand very slowly up and down to drive the mass below the natural frequency. The mass follows the motion of your hand, showing that the mass and the driving force stay 0 degrees out of phase for driving frequencies far below the natural frequency of the oscillator.  Making large amplitude oscillations of your hand show little effect on increasing the amplitude of the mass and spring oscillations.

With the mass hanging at rest, move your hand very rapidly up and down to drive the it 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 and that large amplitude oscillations of your hand have very little effect on increasing the amplitude of the oscillation.

Move your up and down precisley at the natural frequency of oscillation.   The phase relationship for resonance is that motion of the driver (your hand) is 90 degrees ahead of the motion of the oscillator.  With small oscillations of your hand at resonance the mass oscillates with a very large amplitude.

EQUIPMENT:  mass and spring as photographed.

SETUP NOTES: none