You can observe the main effects of resonance with very simple experiments. Hold a spring vertically with a mass suspended
at the other end, and observe the frequency of “free” oscillations with your hand kept still. Then stop the oscillations, and
move your hand extremely slowly up and down in a kind of slow sinusoidal motion. You will see that the mass moves up
and down with the same very low frequency.
(a) How does the amplitude (plus or minus displacement from the center location) of the mass compare with the
amplitude of your hand? (Notice that the phase shift of the oscillation is 0°; the mass moves up when your hand
moves up.)
(b) Next move your hand up and down at a significantly higher frequency than the free-oscillation frequency. How does
the amplitude of the mass compare to the amplitude of your hand? (Notice that the phase shift of the oscillation is
180°; the mass moves down when your hand moves up.)
(c) Finally, move your hand up and down at the freeoscillation frequency. How does the amplitude of the mass compare
with the amplitude of your hand? (It is hard to observe, but the phase shift of the oscillation is 90°; the mass is at the
midpoint of its travel when your hand is at its maximum height.)
(d) Change the system in some way so as to increase the air resistance significantly. For example, attach a piece of paper
to increase drag. At the free-oscillation frequency, how does this affect the size of the response?
A strong dependence of the amplitude and phase shift of the system to the driving frequency is called resonance.