Transcript Slide 1

Lecture 1
Ch15. Simple Harmonic Motion
University Physics: Waves and Electricity
Dr.-Ing. Erwin Sitompul
http://zitompul.wordpress.com
Textbook and Syllabus
Textbook:
“Fundamentals of Physics”,
Halliday, Resnick, Walker,
John Wiley & Sons, 8th Extended, 2008.
Syllabus: (tentative)
Chapter 15: Simple Harmonic Motion
Chapter 16: Transverse Waves
Chapter 17: Longitudinal Waves
Chapter 21: Coulomb’s Law
Chapter 22: Finding the Electric Field – I
Chapter 23: Finding the Electric Field – II
Chapter 24: Finding the Electric Potential
Chapter 26: Ohm’s Law
Chapter 27: Circuit Theory
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Grade Policy
Final Grade = 5% Homework + 30% Quizzes +
30% Midterm Exam + 40% Final Exam +
Extra Points
 Homeworks will be given in fairly regular basis. The average
of homework grades contributes 5% of final grade.
 Homeworks are to be written on A4 papers, otherwise they
will not be graded.
 Homeworks must be submitted on time. If you submit late,
< 10 min.
 No penalty
10 – 60 min.  –40 points
> 60 min.
 –60 points
 There will be 3 quizzes. Only the best 2 will be counted.
The average of quiz grades contributes 30% of final grade.
 Midterm and final exam schedule will be announced in time.
 Make up of quizzes and exams will be held one week after
the schedule of the respective quizzes and exams.
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Grade Policy
 Extra points will be given if you solve a problem in front of the
class. You will earn 1, 2, or 3 points.
 Make up of quizzes and exams will be held one week after
the schedule of the respective quizzes and exams.
 The score of a make up quiz or exam, upon discretion, can be
multiplied by 0.9 (the maximum score for a make up is 90).
Physics 2
Homework 5
Rudi Bravo
009201700008
21 March 2021
No.1. Answer: . . . . . . . .
Heading of Homework Papers (Required)
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Lecture Activities
 The lectures will be held every Wednesday:
18:30 – 21:00 with 15 minutes break if required
 Lectures will be held in the form of PowerPoint
presentations.
 You are expected to write a note along the lectures to record
your own conclusions or materials which are not covered by
the lecture slides.
How to get good grades in this class?
• Do the homeworks by yourself
• Solve problems in front of the class
• Take time to learn at home
• Ask questions
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Lecture Material
 New lecture slides will be available on internet every
Thursday afternoon. Please check the course homepage
regularly.
 The course homepage is :
http://zitompul.wordpress.com
 You are responsible to read and understand the lecture
slides. If there is any problem, you may ask me.
 Quizzes, midterm exam, and final exam will be open-book. Be
sure to have your own copy of lecture slides.
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Simple Harmonic Motion
 The following figure shows a
sequence of “snapshots” of a
simple oscillating system.
 A particle is moving
repeatedly back and forth
about the origin of an x axis.
 One important property of
oscillatory motion is its
frequency, or number of
oscillations that are
completed each second.
 The symbol for frequency is f,
and its SI unit is the hertz
(abbreviated Hz).
1 hertz = 1 Hz
= 1 oscillation per second
= 1 s–1
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Simple Harmonic Motion
 Related to the frequency is the period T of the motion, which
is the time for one complete oscillation (or cycle).
T 
1
f
 Any motion that repeats itself at regular intervals is called
periodic motion or harmonic motion.
 We are interested here only in motion that repeats itself in a
particular way, namely in a sinusoidal way.
 For such motion, the displacement x of the particle from the
origin is given as a function of time by:
x ( t )  x m cos( t   )
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Simple Harmonic Motion
 This motion is called simple
harmonic motion (SHM).
 Means, the periodic motion is a
sinusoidal function of time.
 The quantity xm is called the amplitude of the motion. It is a
positive constant.
 The subscript m stands for maximum, because the amplitude
is the magnitude of the maximum displacement of the
particle in either direction.
 The cosine function varies between ±1; so the displacement
x(t) varies between ±xm.
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Simple Harmonic Motion
 The constant ω is called the angular
frequency of the motion.
 
2
T
 The SI unit of angular frequency is
the radian per second. To be
consistent, the phase constant Φ
must be in radians.
 2 f
  2  f
radians radians cycles

second
cycle second
2  radians  1 cycle  360 
 rad ian 

radian 
2

6
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radian 
1
2
1
4
1
cycle  1 8 0 
cycle  9 0 
cycle  3 0 
12
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Simple Harmonic Motion
x ( t )  x m cos( t )
x ( t )  x m cos( t )
'
x ( t )  x m cos(2  t )
x ( t )  x m cos( t 
Erwin Sitompul

)
4
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Checkpoint
A particle undergoing simple harmonic oscillation of period T is
at xm at time t = 0. Is it at –xm, at +xm, at 0, between –xm and 0,
or between 0 and +xm when:
(a) t = 2T At +xm
(b) t = 3.5T
At –xm
(c) t = 5.25T
At 0
(d) t = 2.8T ?
Between 0 and +xm
0.5T
1.5T
T
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Velocity and Acceleration of SHM
 By differentiating the equation of
displacement x(t), we can find an
expression for the velocity of a particle
moving with simple harmonic motion:
v (t ) 
dx ( t )

dt
d
dt
 x m cos( t   ) 
v ( t )    x m sin( t   )
 Knowing the velocity v(t) for simple
harmonic motion, we can find an
expression for the acceleration of the
oscillating particle by differentiating
once more:
a (t ) 
dv ( t )
dt

d
dt
   x m sin( t   ) 
a ( t )    x m cos( t   )
2
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a (t )   x (t )
2
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Plotting The Motion
Plot the following simple xm
harmonic motions:
0
(a) x1(t) = xmcosωt
(b) x2(t) = xmcos(ωt+π)
–xm
(c) x3(t) = (xm/2)cosωt
(d) x4(t) = xmcos2ωt
x
x1(t)
0.5T
T
x2(t)
m
x1(t)
0
0.5T
T
x3(t)
–xm
xm
0
–xm
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x1(t)
0.5T
T
x4(t)
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Homework 1: Plotting the Motions
xm
Plot the following simple
harmonic motions in three
different plots:
0
(a) xa(t) = xmcosωt
(b) xb(t) = xmcos(ωt–π/2) –xm
(c) xc(t) = xm/2cos(ωt+π/2)
xm
(d) xd(t) = 2xmcos(2ωt+π)
0
xa(t)
0.5T
T
xb(t)?
xa(t)
0.5T
T
xc(t)?
–xm
xm
0
–xm
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xa(t)
0.5T
T
xd(t)?
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Homework 1: Plotting the Motions
New
Plot the following simple harmonic motions in three different
plots:
(a) xa(t) = xmsinωt
(b) xb(t) = xmsin(ωt–π)
(c) xc(t) = xm/2sin(ωt+π/2)
(d) xd(t) = xm/2sin(2ωt+π/2)
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