Physics 218
Lecture 25
Dr. David Toback
Physics 218, Lecture XXV
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Checklist for Today
• Things due earlier this week
– Chapter 15 & 16 in WebCT
– Chapter 18 reading
– Chapter 18 problems for
Recitation
• Today: LAST LECTURE
• Things due Monday
– Chapter 18 in WebCT
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The Schedule
This Week (4/21)
• Monday: Chapter 15 & 16 due in WebCT
• Tues: Reading & Lecture: Chapter 18
• Wed: Recitation on Chapter 18, Lab
• Thurs: Last lecture, Chapter 18
– Not covering Chapter 19
Next Week (4/28)
• No lectures or recitations
• Chapter 18 HW due in WebCT
• Example final problems at
http://faculty.physics.tamu.edu/toback/218/Lectures/FinalReview.pdf
• Finish your HW on WebCT and do the Mini-Practice Exam
Week after that (5/5)
• Final: Monday May 5th, 1PM-3PM in this room
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Next Semester
Some of you continue to ask about next
semester:
• I am NOT teaching 208
• However I am planning on teaching a
new course: “Big Bang, Black Holes,
No Math”
– Intro to Cosmology (PHYS289)
– Based on “A Brief History of Time”
by Stephen Hawking
– If you can’t take it, you might pass
this info along
to friends
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Chap 18 Overview: Oscillations
• Oscillations and vibrations
• Equations of motion
• Simple Model: Mass on a
spring
• Simple Harmonic Motion
• Energy
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Review: Simple Harmonic Motion
Mass on a Spring
Amplitude: Max distance
Period: Time it takes to get
back to here
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Summary: Equation of Motion
Mass m on a spring with spring constant k:
x = A sin(wt + f)
Where
w2 = k/m
A is the Amplitude
f is the “phase”
(phase just allows us to set t=0 when we
want)
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Questions
Simple Harmonic Motion
x = A sin(wt + f)
Can you answer the following:
• What is the amplitude?
• What is the phase?
• What is the angular frequency?
• What is the velocity at the end points?
• What is the velocity at the middle?
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Simple Harmonic Motion
At some level sinusoidal motion is
the definition of Simple
Harmonic Motion
A system that undergoes
simple harmonic motion
is called a
simple harmonic oscillator
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Check:
This looks like a cosine. Makes sense… Spring
and Mass
Paper
which
tells us
what
happens
as a
function
of time
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Mass on a spring with gravity
Take an un-stretched spring. Gently add a
mass and let go. The total stretch from
equilibrium is a distance h before it starts
to rise again. It then oscillates
What is the equation of motion?
Initial
Final
h
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Energy in SHO’s
• Potential Energy for a spring
U = ½kx2
• Kinetic Energy for a block
2
KE = ½mv
• Total Energy
E = U+KE = ½kx2 +½mv2
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Energy Example
A box of mass m is attached to a spring of constant
k, stretched to a distance Xo, held in place and
then and released. Ignore gravity and friction.
As a function of time:
1. What
2. What
3. What
4. What
5. What
is
is
is
is
is
the
the
the
the
the
position?
velocity?
kinetic energy?
potential energy?
total energy of the system?
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Understanding Phase: Initial Conditions
A block with mass m is attached to the
end of a spring, with spring constant k.
The spring is stretched a distance D
and let go at t=0
– What is the position of the mass at
all times?
– Where does the maximum speed
occur?
– What is the maximum speed?
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Example: Spring with a Push
We have a spring system
– Spring constant: K
– Mass: M
– Initial position: X0
– Initial Velocity: V0
Find the position at all times
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Challenge Exam
• Announcement of this semester’s 218 Challenge
Exam: Monday April 28th at 6:00PM
– Not required (just for fun)
– Does not (will not!!!) count as part of your
final grade
• Test your skills against the best Aggies from all
the Physics 218 sections (not just this lecture)
on Physics 218 material
• Students who perform well will be recognized as
Mechanics Scholars, and honored at a banquet in
their honor. Other prizes, including cash.
• Handout information on my WebSite
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That’s it!
• Next Week:
– No classes or Recitations
– HW for Chapter 18 due
– Example final problems at
http://faculty.physics.tamu.edu/toback/218/Lectures/FinalReview.pdf
– Finish your HW on WebCT, do the Mini-Practice Exam
• Final: Monday May 5th, 1PM-3PM in this room
– Chapters 14 -16 and 18 will be on the final
– I guarantee a problem from each
• Good luck studying for Finals!
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Uniform Circular Motion
It turns out Uniform
Circular Motion is really
Simple Harmonic Motion
but in two dimensions
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Uniform Circular Motion in 2D
A ball is moving anti-clockwise in uniform
circular motion with a radius R and
speed V. At t=0 we set Q0=0.
1. What is the equation of motion for Q?
2. What is the equation of motion in the x
direction?
3. What is the displacement at all times?
4. What is the velocity at all times?
5. What is the speed at all times?
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Pendulums
• Pendulums can
be a pretty
good Simple
Harmonic
Oscillator
• The amount of
swing has to be
small
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Example: Pendulum
For small swing
(q small) show
that the
motion of a
ball on a
pendulum is
simple
harmonic
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Period of a Pendulum
Show that the period of
a pendulum doesn’t
depend on the mass.
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Coming up…
• Thursday: Last class meeting
– Review for the final, we’ll skip Chapter 15
– Do all the problems on the handout before class
– Be prepared to vote for which type of problem you want
to review most
• Monday December 11th Final Exam, 1PM. Here
– The material in Chapters 12 and 13 will be on the final
– I guarantee there will be at least one problem from
each chapter on the final
• Homework 13 and FCI II are due Wednesday
• A 100% on all homework is required in order to pass the
class
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Next Lecture
• Notes on the final:
– Chapter 14 will be on the final.
– Nothing from Chapter 15 on the final.
– I guarantee there will be at least one
problem from these last two weeks on
the final
– Final is Monday Dec 15th, 1:00PM3:00PM, here
• Next time
– Review
Physics
218, Lecture
XXV
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– Come prepared
with
questions
Draw position as a function of
Time?
Spring
and Mass
Paper
which tells
us what
happens
as a
function
of time
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Ballistic Pendulum
• A bullet plows into a
block of wood which is
part of a pendulum.
• We know m, M and v.
• How high, h, does the
block of wood go?
• What is the equation of
motion after the
collision?
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Some Useful Relations and Weird
Results
As we' ve seen the angular ve locity w
is related to the Period T by :
2
2
w
T
T
w
k
m
2
But w   T  2
m
k
Period doesn' t depend on the amplitude
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Doing a mass on a spring with g
Take an un-stretched spring with constant
k. Add a mass, m. Slowly stretch to -x0,
and bring to rest and let go.
What is the equation of motion?
Add a mass
Stretch
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