Chapter 13: Energy Flow and Power
 13.1 Harmonic Motion
 13.2 Why Things Oscillate
 13.3 Resonance and Energy
Chapter 13 Objectives
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Identify characteristics of harmonic motion, such as cycles, frequency,
and amplitude.
Determine period, frequency, and amplitude from a graph of harmonic
motion.
Use the concept of phase to compare the motion of two oscillators.
Describe the characteristics of a system that lead to harmonic motion.
Describe the meaning of natural frequency.
Identify ways to change the natural frequency of a system.
Explain harmonic motion in terms of potential and kinetic energy.
Describe the meaning of periodic force.
Explain the concept of resonance and give examples of resonance.
Chapter 13 Vocabulary Terms
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amplitude
damping
frequency
harmonic motion
hertz (Hz)
natural frequency
oscillator
period
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periodic force
periodic motion
phase
phase difference
piezoelectric effect
resonance
stable equilibrium
unstable equilibrium
Inv 13.1 Harmonic motion
Investigation Key Question:
How do we describe the back
and forth motion of a
pendulum?
13.1 Cycles, systems, and oscillators
A cycle is a unit of motion that repeats.
13.1 Harmonic motion is common
sound
communications
nature
clocks
13.1 Describing harmonic motion
 The period of an oscillator is
the time to complete one
cycle.
13.1 Describing harmonic motion
 Frequency is closely
related to period.
 The frequency of an
oscillator is the number
of cycles it makes per
second.
At a frequency of 100 Hz, an
oscillating rubber band
completes 100 cycles per sec.
13.1 Describing harmonic motion
 The unit of one cycle per second is called a
hertz (Hz).
 When you tune into a station at 100.6 on the FM
dial, you are setting the oscillator in your radio
to a frequency of 100.6 megahertz (MHz).
13.1 Amplitude
 Amplitude describes the size of a cycle.
 The value of the
amplitude is the
maximum amount the
system moves away from
equilibrium.
13.1 Amplitude
 The energy of an oscillator is proportional to
the amplitude of the motion.
 Friction drains energy away from motion and
slows the pendulum down.
 Damping is the term used to describe this loss.
13.1 Harmonic Motion Graphs
 Graphs of linear motion do not show cycles.
13.1 Harmonic motion graphs
 Graphs of harmonic motion repeat every period,
just as the motion repeats every cycle.
 Harmonic motion is sometimes called periodic
motion.
13.1 Circles and the phase of harmonic
motion
 Circular motion is very similar
to harmonic motion.
 Rotation is a cycle, just like
harmonic motion.
 One key difference is that cycles
of circular motion always have a
length of 360 degrees.
13.1 Circles and the phase
of harmonic motion
 The word “phase” means where the oscillator is in the
cycle.
 The concept of phase is important when comparing one
oscillator with another.
Chapter 13: Energy Flow and Power
 13.1 Harmonic Motion
 13.2 Why Things Oscillate
 13.3 Resonance and Energy
Inv 13.2 Why Things Oscillate
Investigation Key Question:
What kinds of systems
oscillate?
13.2 Why Things Oscillate
 Systems that have harmonic
motion move back and forth
around a central or
equilibrium position.
 Equilibrium is maintained by
restoring forces.
 A restoring force is any force
that always acts to pull the
system back toward
equilibrium.
13.2 Inertia
 Newton’s first law explains why harmonic motion
happens for moving objects.
 According to the first law, an object in motion stays in
motion unless acted upon by a force.
13.2 Stable and unstable systems
 Not all systems in equilibrium show harmonic motion
when disturbed.
 In unstable systems there are forces that act to pull the
system away from equilibrium when disturbed.
 Unstable systems do not usually result in harmonic
motion (don't have restoring forces).
13.2 The natural frequency
 The natural frequency is
the frequency at which
systems tend to oscillate
when disturbed.
 Everything that can
oscillate has a natural
frequency, and most
systems have more than
one.
Adding a steel nut greatly increases the inertia of a stretched rubber
band, so the natural frequency decreases.
13.2 Changing the natural frequency
 The natural frequency is proportional to the acceleration
of a system.
 Newton’s second law can be applied to see the
relationship between acceleration and natural frequency.
Chapter 13: Energy Flow and Power
 13.1 Harmonic Motion
 13.2 Why Things Oscillate
 13.3 Resonance and Energy
Inv 13.3 Resonance and Energy
Investigation Key Question:
What is resonance and why is it important?
13.3 Resonance and Energy
 Harmonic motion involves both potential energy and
kinetic energy.
 Oscillators like a pendulum, or a mass on a spring,
continually exchange energy back and forth between
potential and kinetic.
13.3 Resonance
 A good way to understand resonance is to
think about three distinct parts of any
interaction between a system and a force.
13.2 Resonance
 Resonance occurs when the frequency of a
periodic force matches the natural frequency of
a system in harmonic motion.
13.3 Energy, resonance and damping
 Steady state is a balance between damping from
friction and the strength of the applied force.
 Dribbling a basketball on a
floor is a good example of
resonance with steady
state balance between
energy loss from damping
and energy input from
your hand.
Quartz Crystals
 The precise heartbeat of nearly all modern electronics is a
tiny quartz crystal oscillating at its natural frequency.
 In 1880, Pierre Curie and his brother Jacques discovered
that crystals could be made to oscillate by applying
electricity to them.
 This is known as the piezoelectric effect.