Transcript SHM Part 2

SHM is the projection of uniform
circular motion
The ball mounted on the turntable moves in uniform circular motion, and its
shadow, projected on a moving strip of film, executes simple harmonic motion.
Phase of SHM
SHM is the projection of uniform circular motion on a line in the plane of
the motion. One period of SHM can be divided into 3600.
Tone
Quality
(Timbre)
http://www.phy.ntnu.edu.tw/ntnujava/index.php?topic=17
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.
Shock Absorber
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.
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.
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.
Damped and Driven
Harmonic Motion
Greatest Tides in the World
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 Bay of Fundy,
shown on the east
coast of North America
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.