periodic motion - ucsb · shining a flashlight on a candle placed on a rotating lazy-susan spice...

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


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


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.


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.


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.


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.


Characteristics of SHM

• Frequency, period, amplitude … see pages 423–424.

• Consider Example 13.2 and Figure 13.8.


X versus t for SHO then simple variations on a theme


SHM phase, position, velocity, and acceleration

• SHM can occur with

various phase angles.

• For a given phase we can examine

position, velocity, and acceleration.


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.


Energy in SHM

• Energy is conserved during SHM and the forms (potential and

kinetic) interconvert as the position of the object in motion

changes.


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.


Energy and momentum are related in SHM

• Refer to Example 13.5.

• Figure 13.16 illustrates

the example.


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.


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.


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.


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.


Damped oscillations II


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.


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.


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).

periodic motion - ucsb · shining a flashlight on a candle placed on a rotating lazy-susan spice...

Documents