Transcript Chapter 18: Harmonic Motion

Vibrations, Waves and Sound
Unit 7: Vibrations, Waves & Sound
Chapter 18: Harmonic Motion
 18.1
Harmonic Motion
 18.2
Graphs of Harmonic Motion
 18.3
Properties of Oscillators
18.1 Investigation: Harmonic Motion and the
Pendulum
Key Question:
How do we describe the backand-forth motion of a
pendulum?
Objectives:

Measure the amplitude and period of a pendulum.
Describe any oscillator in terms of frequency, period, amplitude,
and phase.
 Learn to read and represent frequency, period, amplitude, and
phase on a graph.

Harmonic motion
A.
Linear motion gets us
from one place to
another.
B.
Harmonic motion is
motion that repeats
over and over.
Harmonic motion
 A pendulum
is a device that swings back and
force.

A cycle is one unit of harmonic motion.
Oscillators
 An
oscillator is a physical
system that has repeating
cycles or harmonic motion.
 Systems
that oscillate move
back and forth around a
center or equilibrium position.
 The
term vibration is another
word used for back and forth
motion.
Systems and oscillations
 Our
solar system is a large
oscillator with each planet in
harmonic motion around the
Sun.
 Earth
is a part of several
oscillating systems.
Sound oscillations
 As
a speaker cone
moves back and
forth, it pushes and
pulls on air,
creating oscillating
changes in
pressure that we
can detect with our
ears.
Harmonic motion
 Harmonic
motion can be fast or slow, but speed
constantly changes during its cycle.
 We
use period and frequency to describe how
quickly cycles repeat themselves.
 The
time for one cycle to occur is called a period.
Harmonic motion

The frequency is the number of
complete cycles per second.

Frequency and period are inversely
related.

One cycle per second is called a hertz,
abbreviated (Hz).

For a radio to play a specific station, the
frequency of the oscillator in the radio
must match the frequency of the
oscillator signal.
Calculating frequency
The period of an oscillator is 15 minutes.
What is the frequency of this oscillator in hertz?
1.
Looking for: …the frequency in hertz.
2.
Given: …the period (15 min).
3.
Relationships: Use conversion factors
and formula: ƒ = 1/T.
4.
Solution: Convert min. to sec:
15 min x 60 s = 900 s ƒ = 1 cycle = 0.0011 Hz
1 min
900 s
Amplitude
 Amplitude
describes the
“size” of a cycle.
 The
amplitude is the
maximum distance the
oscillator moves away
from its equilibrium
position.
Amplitude
 A pendulum
with an
amplitude of 20 degrees
swings 20 degrees away
from the center in either
direction.
 We
use the word damping
to describe the gradual loss
of amplitude of an oscillator
such as a pendulum.
Damping

Friction slows a pendulum down, just as it slows all motion.

If you wanted to make a clock with a pendulum, you would
have to find a way to keep adding energy (through winding
or electricity) to counteract the damping of friction.
Unit 7: Vibrations, Waves & Sound
Chapter 18: Harmonic Motion
 18.1
Harmonic Motion
 18.2
Graphs of Harmonic Motion
 18.3
Properties of Oscillators
18.2 Investigation: Harmonic Motion Graphs
Key Question:
How do we make graphs of
harmonic motion?
Objectives:

Construct graphs of harmonic motion.
Interpret graphs of harmonic motion to determine phase,
amplitude, and period.
 Use the concept of phase to describe the relationship between
two examples of harmonic motion.

Graphs of harmonic motion
 A graph
is a good way to
show harmonic motion
because you can quickly
recognize cycles.
 Graphs
of linear motion
do not show cycles.
Determining period from a graph
 To
find the period from a
graph, start by identifying
one complete cycle.
 The
cycle must begin
and end in the same
place in the pattern.
 Subtract
the beginning
time from the ending
time.
Determining amplitude from a graph
 On
a graph of harmonic
motion, the amplitude is
half the distance
between the highest and
lowest points on the
graph.
 The
amplitude is 20 cm.
Phase
 The
phase tells you exactly where an oscillator is in
its cycle.
 Circular
motion is a kind of harmonic motion because
rotation is a pattern of repeating cycles.
 Because
circular motion always has cycles of 360
degrees, we use degrees to measure phase.
Phase and harmonic motion graphs

Imagine a peg on a rotating
turntable.

A bright light casts a shadow of
the peg on the wall. As the
turntable rotates, the shadow
goes back and forth on the wall.

If we make a graph of the
position of the shadow, we get a
harmonic motion graph.
Pendulums in phase
 The
concept of phase is most important when
comparing two or more oscillators.
 We
say these pendulums are in phase because their
cycles are aligned.
Pendulums out of phase by 90o
 Although,
they have the
same cycle, the first
pendulum is always a little
bit ahead in its cycle
compared to the second
pendulum.
 The
pendulums are out of
phase by 90 degrees.
Pendulums out of phase by 180o
 Two
oscillators that are
180 degrees out of phase
are one-half cycle apart.
 When
pendulum number
1 is all the way to the left,
pendulum number 2 is all
the way to the right.
Unit 7: Vibrations, Waves & Sound
Chapter 18: Harmonic Motion
 18.1
Harmonic Motion
 18.2
Graphs of Harmonic Motion
 18.3
Properties of Oscillators
18.3 Investigation: Natural Frequency
Key Question:
What kinds of systems oscillate?
Objectives:

Build a mechanical oscillator and find its period and natural
frequency.

Change the natural frequency of an oscillator.
Systems and equilibrium
 Systems
that have harmonic motion always move
back and forth around a central, or equilibrium
position.
Restoring force
 A restoring
force is any force that always acts to
pull a system back toward equilibrium.
Restoring force and inertia
 A restoring
force keeps a
pendulum (or child)
swinging.
 The
restoring force is
related to the weight of
the mass and the lift force
(or tension) of the string
supporting the mass.
Harmonic motion and machines
 Mechanical
systems usually do
not depend on a restoring force
or inertia.
 The
piston in a car engine is
harmonic motion, but the
motion is caused by the
rotation of the crankshaft and
the attachment of the
connecting rod.
Natural frequency and resonance
 The
natural frequency is
the frequency (or period) at
which a system naturally
oscillates.
 Every
system that oscillates
has a natural frequency.
Natural frequency
 Every
oscillating system has a
natural frequency.
 Microwave
ovens, musical
instruments, and cell phones are
common devices that use the
natural frequency of an oscillator.
 The
strings of a guitar are tuned
by adjusting the natural frequency
of vibrating strings to match
musical notes.
Natural frequency and resonance
 You
can get a swing moving
by pushing it at the right
time every cycle.
 A force
that is repeated over
and over is called a
periodic force.
Natural frequency and resonance
 Resonance
happens
when a periodic force has
the same frequency as the
natural frequency.
 When
each push adds to
the next one, the
amplitude of the motion
grows.
Jump rope
 A jump
rope depends on
resonance.
 If
you shake it at the
right frequency, it makes
a wave.
 If
the frequency is too
fast or too slow, the rope
will not make the wave
pattern at all.
Simple oscillators
 A mass
on a spring is
an oscillating system.
 When
the spring is
compressed, it pushes
the mass back to
equilibrium.
 When
the spring is
extended, it pulls the
mass back toward
equilibrium.
Simple oscillators

A vibrating string oscillator is a
rubber band stretched between
two rods.

If the middle of the rubber band is
pulled to the side, it will move
back toward equilibrium when it is
released.

Stretching the rubber band to the
side creates a restoring force.

When the rubber band is
released, inertia carries it past
equilibrium and it vibrates.
Skyscrapers and Harmonic Motion

The John Hancock Tower is one
of the tallest skyscrapers in New
England.

While this skyscraper was being
built in 1972 and 1973, a disaster
struck— windowpanes started
falling out all over the building
and crashing to the ground.