10.4

1
10.4 The Pendulum
2
Period of a Simple Pendulum
3
10.5. Damped Harmonic Motion
In simple harmonic motion, an object oscillates
with a constant amplitude. In the presence of
energy dissipation, the amplitude of oscillation
decreases as time passes, and the motion is
referred to as damped harmonic motion.
4
Shock Absorber
5
Degree of Damping
The degree of damping increases from curve 1 to
curve 5. Curve 1 represents undamped or simple
harmonic motion. Curves 2 and 3 show underdamped
motion. Curve 4 represents critically damped
harmonic motion. Curve 5 illustrates overdamped
motion. Typical automobile shock absorbers are
designed to produce underdamped motion somewhat
like that in curve 3.
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10.6 Driven Harmonic Motion and Resonance
To set an object on an ideal spring into simple
harmonic motion, some agent must apply a force
that stretches or compresses the spring
initially. Suppose that this force is applied at
all times, not just for a brief initial moment.
The resulting motion is known as driven harmonic
motion, because the additional force drives or
controls the behavior of the object to a large
extent. The additional force is identified as the
driving force.
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Resonance
Resonance occurs when the frequency of the
driving force (blue arrows) matches a frequency
at which the object naturally vibrates. The red
arrows represent the velocity of the object.
8
Greatest Tides in the World
Figure 10.27  The Bay of Fundy at (a) high tide
and (b) low tide. In some places the water level
changes by almost 15 m.
This phenomenon is partly due to resonance. The
time, or period, that it takes for the tide to
flow into and ebb out of a bay depends on the
size of the bay, the topology of the bottom, and
the configuration of the shoreline. The ebb and
flow of the water in the Bay of Fundy has a
period of 12.5 hours, which is very close to the
lunar tidal period of 12.42 hours. The tide then
drives water into and out of the Bay of Fundy
at a frequency (once per 12.42 hours) that nearly
matches the natural frequency of the bay (once
per 12.5 hours). The result is the extraordinary
high tide in the bay.