Course Information
Physics 1C
Waves, optics and modern
physics
Instructor: Melvin Okamura
email: mokamura@physics.ucsd.edu
Class Schedule
• Lectures
– Mon. Wed. Fri. 9:00-9:50 pm WLH 2005
• Quizzes
– Alternate Fri. (Starting the 3rd Friday)
– 9:00-9:50 pm WLH 2005
• Problem Session
– TBA
Homework
• Homework will be assigned each week.
• Homework will not be graded but quiz
questions will resemble the homework.
• Solutions to the homework problems will
be posted on the web page.
Course Syllabus on the web page http://physics.ucsd.edu/
students/courses/winter2009/physics1c
Instructor: Mel Okamura – mokamura@physics.ucsd.edu
Office: 1218 Mayer Hall
Office Hrs. Thu 2-3 pm or by appointment
TA: Alexander Mendez, ajmendez@physics.ucsd.edu,
Office: TBA
Office Hrs: TBA
Text. Physics 1 Serway and Faughn, 7th edition, UCSD custom
edition.
Grades
• Bi-weekly quizzes (4) will be held on
Friday. You are allowed to drop 1 quizzes.
There will be no make-up quizzes.
• Final exam covering the whole course.
• The final grade will be based on
Quizzes 60% (best 3 out of 4 quizzes)
Final exam 40%
Extra credit 5% (clicker responses)
Clickers
Interwrite Personal Response System (PRS)
Available at the bookstore
Clicker questions will be asked during class. Student
responses will be recorded.
2 points for each correct answer
1 point for each incorrect answer.
The clicker points (up to 5% ) will be added to your score
at the end of the quarter
1
Laboratory
• The laboratory is a separate class which
will be taught by Professor Anderson.
Waves and Modern Physics
• 1-2 Oscillations and Waves
– Sound, light, radio waves, microwaves
• 3-5 Optics
– Lenses, mirrors, cameras, telescopes.
• 6 Physical Optics
– Interference, diffraction, polarization
• 7-9 Quantum Mechanics
– Quantum mechanics, atoms, molecules, transistors,
lasers
• 10 Nuclear Physics
– Radioactivity, nuclear energy
1.1 Oscillations
•
•
•
•
•
Kinematics - sinusoidal waves
Dynamics -Newton’s law and Hooke’s law.
Energetics – Conservation of Energy
Mass on a spring
Pendulum
Description of Oscillatory Motion
Mass on a spring. Stretch and Release How does the displacement vary with time?
Equilibrium
position
Oscillations
• repetitive displacements with a time period
• provide the basis for measuring time
• serve as the starting point for describing
wave motion.
• Example- Mass on a spring
Simple Harmonic Motion
• The motion is called simple harmonic
motion
+
Displacement 0
-
x
Displacement from
Equilibrium position
Time ->
• Positive and negative displacements – Average is zero
• Periodic (i.e. repeating) in time
2
Motion is a Sinusoidal Function
T
Displacement
The oscillation follows a sinusoidal
function
Time
x = A cos ωt
Amplitude - A (maximum displacement, m)
Period - T ( repeat time, s)
1
Cycles/s (Hertz)
Frequency - f =
T
Angular Frequency ω = 2πf = (radians /s)
Phase shift
T
x
The projection of the rotating vector A on the x axis gives
x = A cos(θ) = A cos(
2π
t) = A cos(2πft) = A cos(ωt)
T
θ is the phase angle (radians) which increases with
increasing t (θ=0 at t=0 for cos function)
f is the frequency (cycles/s)
ω is the angular frequency (radians/s)
Dynamics of a Mass on a spring
Hooke’s Law – The Force
exerted by spring is
proportional to the
displacement from the
equilibrium position.
∆t
G
G
F = −kx
time
∆θ = 2π
phase shift
∆t
T
radians
k - Force constant
Units N/m
Used when comparing two oscillations.
Hooke’s Law
(magnitudes)
F= kx
Force
The force of gravity is
cancelled by the force
of the spring.
slope =k
displacement
The force is linearly related to the displacement.
The slope is constant
Vertical direction
Equilibrium
position
y
Fy
The force on the object when it is displaced upward
by a distance y from the equilibrium position is only
due to the spring.
JJG
G
Fy = −ky
3
displacement, velocity acceleration
Newton’s Law applied to mass on
spring
G
a
x = A cos(ωt)
v=
dx
= −ωA sin(ωt)
dt
a=
dv
= −ω2 A cos(ωt)
dt
JG
G
Fs = ma
Fs = −kx = −kA cos ωt
ma = −mω A cos ωt
2
gives
x, v and a are sinusoidal functions with different initial
phase angles.
The magnitudes of v and a are multiplied by ω or ω2 to
preserve the units.
Demo
How does the period depend on mass?
ω=
k
m
f=
1 k
2π m
}
For sinusoidal
motion.
m
k
T = 2π
Energy
Energy required to stretch (compress) a spring by
a displacement x
F
E=
How does the period depend on the force
constant?
1 2
kx
2
Work = Faverage x
F
Faverage =½ kx
How does the period depend on the
amplitude?
x
Note the energy depends on x2 so it is independent of
the sign of x, i.e. same for compression and stretch.
Question
Oscillation between KE and PE
Total energy =KE+PE = constant
Find an expression for the maximum velocity for a
mass on a spring that is stretched with amplitude A and
Has frequency f.
PEmax
KEmax
KEmax
KEmax
PEmax = KEmax
PEmax
PEmax
1 2 1
2
kA = mv max
2
2
A
v max
k
A = ωA = 2πfA
=
m
0
4
Pendulum
The restoring force is proportional
to the displacement
for small displacements.
F = −mgsin θ
F = −mgθ for small θ
F=−
mg
s
L
Equivalent to Hooke’s Law with k=mg/L
ω=
ω=
k
m
g
L
Demo
Pendulum oscillations.
How does the period depend on L?
How does the period depend on M?
then becomes
T = 2π
L
g
The period is dependent on L
but independent of m
5