Chapter 13: Harmonic Motion
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Transcript Chapter 13: Harmonic Motion
Chapter 13: Energy Flow and Power
13.1 Harmonic Motion
13.2 Why Things Oscillate
13.3 Resonance and Energy
Chapter 13 Objectives
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
amplitude
damping
frequency
harmonic motion
hertz (Hz)
natural frequency
oscillator
period
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.