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Copyright © 2008 Pearson Education Inc., publishing as Pearson Addison-Wesley
PowerPoint® Lectures for
University Physics, Twelfth Edition
– Hugh D. Young and Roger A. Freedman
Lectures by James Pazun
Chapter 13
Periodic Motion
Copyright © 2008 Pearson Education Inc., publishing as Pearson Addison-Wesley
Goals for Chapter 13
• To outline periodic motion
• To quantify simple harmonic motion
• To explore the energy in simple harmonic motion
• To consider angular simple harmonic motion
• To study the simple pendulum
• To examine the physical pendulum
• To explore damped oscillations
• To consider driven oscillations and resonance
Copyright © 2008 Pearson Education Inc., publishing as Pearson Addison-Wesley
Introduction
• If you look to the right,
you’ll see a time-lapse
photograph of a simple
pendulum. It’s far from
simple, but it is a great
example of the regular
oscillatory motion we’re
about to study.
Copyright © 2008 Pearson Education Inc., publishing as Pearson Addison-Wesley
Describing oscillations
• The spring drives the glider back and forth on the air-track and you can observe the changes in the free-body diagram as the motion proceeds from –A to A and back.
• Refer to Example 13.1.
Copyright © 2008 Pearson Education Inc., publishing as Pearson Addison-Wesley
Simple harmonic motion
• An ideal spring responds to stretch and compression linearly, obeying Hooke’s Law.
• For a real spring,
Hookes’ Law is a good
approximation.
Copyright © 2008 Pearson Education Inc., publishing as Pearson Addison-Wesley
Simple harmonic motion viewed as a projection
• If you illuminate uniform circular motion (say by shining a flashlight on a candle placed on a rotating lazy-Susan spice rack), the shadow projection that will be cast will be undergoing simple harmonic motion.
Copyright © 2008 Pearson Education Inc., publishing as Pearson Addison-Wesley
Characteristics of SHM
• Frequency, period, amplitude … see pages 423–424.
• Consider Example 13.2 and Figure 13.8.
Copyright © 2008 Pearson Education Inc., publishing as Pearson Addison-Wesley
X versus t for SHO then simple variations on a theme
Copyright © 2008 Pearson Education Inc., publishing as Pearson Addison-Wesley
SHM phase, position, velocity, and acceleration
• SHM can occur with
various phase angles.
• For a given phase we can examine
position, velocity, and acceleration.
Copyright © 2008 Pearson Education Inc., publishing as Pearson Addison-Wesley
Watch variables change for a glider example
• As the glider
undergoes SHM, you
can track changes in
velocity and
acceleration as the
position changes
between the classical
turning points.
• Refer to Problem-
Solving Strategy 13.1
and Example 13.3.
Copyright © 2008 Pearson Education Inc., publishing as Pearson Addison-Wesley
Energy in SHM
• Energy is conserved during SHM and the forms (potential and
kinetic) interconvert as the position of the object in motion
changes.
Copyright © 2008 Pearson Education Inc., publishing as Pearson Addison-Wesley
Energy in SHM II
• Figure 13.15 shows the interconversion of kinetic and potential
energy with an energy versus position graphic.
• Refer to Problem-Solving Strategy 13.2.
• Follow Example 13.4.
Copyright © 2008 Pearson Education Inc., publishing as Pearson Addison-Wesley
Energy and momentum are related in SHM
• Refer to Example 13.5.
• Figure 13.16 illustrates
the example.
Copyright © 2008 Pearson Education Inc., publishing as Pearson Addison-Wesley
Angular SHM
• Watches keep time based on regular oscillations of a
balance wheel initially set in motion by a spring.
• Figure 13.19 illustrates the delicate inner mechanism of
a clock or watch.
Copyright © 2008 Pearson Education Inc., publishing as Pearson Addison-Wesley
Vibrations of molecules
• Two atoms separated by their internuclear distance r can be
pondered as two balls on a spring. The potential energy of such a
model is constructed many different ways. The Leonard–Jones
potential shown as Equation 13.25 is sketched in Figure 13.20
below. The atoms on a molecule vibrate as shown in Example
13.7.
Copyright © 2008 Pearson Education Inc., publishing as Pearson Addison-Wesley
Dinosaurs, long tails, and the physical pendulum
• The stride of Tyrannosaurus rex can be treated as a
physical pendulum. Refer to Example 13.10 and Figure
13.24 below.
Copyright © 2008 Pearson Education Inc., publishing as Pearson Addison-Wesley
Damped oscillations
• A person may
not wish for the
object they study
to remain in
SHM. Consider
shock absorbers
and your
automobile.
Without damping
the oscillation,
hitting a pothole
would set your
car into SHM on
the springs that
support it.
Copyright © 2008 Pearson Education Inc., publishing as Pearson Addison-Wesley
Damped oscillations II
Copyright © 2008 Pearson Education Inc., publishing as Pearson Addison-Wesley
The physical pendulum
• A physical
pendulum is any
real pendulum
that uses an
extended body in
motion. Figure
13.23 illustrates a
physical
pendulum and
you may wish to
refer to it as you
consider
Example 13.9.
Copyright © 2008 Pearson Education Inc., publishing as Pearson Addison-Wesley
Forced (driven) oscillations and resonance
• A force applied “in synch” with a motion already in progress
will resonate and add energy to the oscillation (refer to Figure
13.28).
• A singer can shatter a glass with a pure tone in tune with the
natural “ring” of a thin wine glass.
Copyright © 2008 Pearson Education Inc., publishing as Pearson Addison-Wesley
Forced (driven) oscillations and resonance II
• The Tacoma Narrows Bridge suffered spectacular structural
failure after absorbing too much resonant energy (refer to Figure
13.29).