3a60.47 Driven Mass and Spring

PURPOSE: To demonstrate resonance.

DESCRIPTION: A mass is connected by two springs.  One spring is fixed to a bar and the other is clamped to a mechanical vibrator.  A function generator controls the mechanical vibrator.  Keep the amplitude of the driver constant while the frequency is adjusted.  When the oscillation of the driver matches the natural frequency of the system the response of the system will show a very large amplitude.

Note that the tension of the height of the springs will determine the natural frequency.

Displace the mass and let it oscillate naturally.  Carefully observe the natural frequency and the damping, with no sustained oscillation.

Adjust the vibrator to drive the system below the natural frequency. The mass follows the motion of the vibrator, 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 with the vibrator will show little effect on increasing the amplitude of the oscillations.

Adjust the vibrator to drive the mass above the natural frequency.  The mass moves opposite to the motion of the vibrator, 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 have very little effect on increasing the amplitude of the pendulum oscillation.

Adjust the vibrator at the natural frequency of oscillation.   The phase relationship for resonance is that motion of the driver is 90 degrees ahead of the motion of the oscillator.  With small oscillations at resonance the mass oscillates with a very large amplitude.

EQUIPMENT:  Mass, two springs, function generator, mechanical vibrator as photographed.

SETUP NOTES: The mass and springs are stored in mechanics.