lecture 2 - physics vibrations and waves (8.03)

physics vibrations and waves

1. Physics 8.03 Physics 8.03
Vibrations and Waves Vibrations and Waves
Lecture 2 Lecture 2

2. Problem Set #1 Problem Set #1
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What What’’s on it? s on it?
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Three problems on complex notation and Three problems on complex notation and
superposition superposition
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Two on simple harmonic oscillators Two on simple harmonic oscillators
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One on damped harmonic oscillator One on damped harmonic oscillator
(Need to make a (Need to make a matlab matlab plot) plot)

3. More organizational things More organizational things
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Text books Text books
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Vibrations and Waves Vibrations and Waves , by French (required) , by French (required)
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Nearly every page used in 8.03 Nearly every page used in 8.03
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EM vibrations, waves and radiation EM vibrations, waves and radiation , by , by Bekefi Bekefi and and
Barrett (required) Barrett (required)
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Lots of jumping around, pay attention to reading Lots of jumping around, pay attention to reading
assignments assignments
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Optics Optics, by Hecht (recommended) , by Hecht (recommended)
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Useful for Polarization, Interference, Diffraction Useful for Polarization, Interference, Diffraction

4. More organizational things More organizational things
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Grades on the web Grades on the web
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Part of a pilot system of web Part of a pilot system of web --based grade database based grade database
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Ready in mid Ready in mid--February February
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Anonymous (or otherwise) feedback Anonymous (or otherwise) feedback
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I will respond I will respond ��Πbe constructive be constructive
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I will post your comments (anonymously) along with I will post your comments (anonymously) along with
my response my response ��Πavoid profanity avoid profanity

5. Last time: Simple harmonic motion Last time: Simple harmonic motion
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Equation of Motion Equation of Motion
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Solutions in three forms Solutions in three forms
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Quadratic potential Quadratic potential
��ΠSHMSHM
0
2
0 2
2
= + x
dt
xd
ω
] . Re[
) sin( ) cos( )(
) cos(
) (
0 0
0
0
φ ω
ω ω
φ
ω
+
=
+ =
+
=
t j
eA
t B t A tx
t A
2
2
1
)(
)(
)(
kx xU
kx xF
dx
x dU
= ⇒
−= = −

6. DAMPED DAMPED HARMONIC MOTION HARMONIC MOTION
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Finish up simple harmonic motion Finish up simple harmonic motion
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Conservative forces, quadratic potentials and SHM Conservative forces, quadratic potentials and SHM
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Approximate Approximate SHOs SHOs: the pendulum : the pendulum
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Add damping term to equation of motion Add damping term to equation of motion
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Solutions depend on size of the damping Solutions depend on size of the damping
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Lightly damped (under Lightly damped (under--damping) damping)
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Heavily damped (over Heavily damped (over--damping) damping)
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Critically damped Critically damped