@kul 1 shm
TRANSCRIPT
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GETARAN
AP Physics Chttp://www.jca.umbc.edu/~george/html/courses/phys224/2006spg/lectures/
FENOMENA ALAM,
PEMODELAN & DESKRIPSI FISIS
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GETARAN: definisi
Gerak tidak menjalartetapi memiliki pola ke-
berulang-andisekitar titik setimbang
yang ditinjau
Obyek Besaran Fisis
Gerak
benda masif(berukuranbesar/kasatmata) yangmengalamigerak bolak-
balikdisekitar titiksetimbang
posisi (x) (?)
Persamaangerak bolak-balik
kecepatan (v)
percepatan (a)
energi (E)
Pola ke-berulang-an
frekuensi (f) periode (T)
periodik: sinus/cosinus
tidak periodik (tidak dibahas)
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Oscillatory Motion is repetitive back and forth motionabout an equilibrium position
Oscillatory Motion isperiodic.
Swinging motion and vibrations are forms ofOscillatory Motion.
Objects that undergo Oscillatory Motion are called
Oscillators.
GETARAN: terminologi (per-istilah-an)
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FENOMENA ALAM: getaran teratur & acak
Contoh fenomena alam
dengan sifat gerak berulangyang teratur dan memenuhi
definisi gerak selaras
sederhana
Bila berlangsung pelan, fenomena
gerak ini dapat memenuhi kriteria
selaras sederhana, namun
kenyataannya tidaklah selalu
sederhana
Ilustrasi manakah (kiri / kanan) yang sesuai dengan definisi
gerak bolak-balik (getaran) sesuasi dengan definisi?
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EFEK (TERLIHAT) FENOMENA ALAM GETARAN: Gempa Vulkanik
Proses erupsi yang didahuluidengan gempa vulkanik
merupakan hasil dari getaran
hebat dapur magma yang dapat
dirasakan di sekitar area gunung
getaran hebat dapur magma yangdapat dirasakan hingga permukaan
ditangkap dengan seismograp.
Berakibat munculnya rekahan di
permukaan dan/atau di bawah
permukaan
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We use natural oscillations to measure time
1.pendulum
2.quartz crystals
Currently, we define 1 second based on
oscillations inside a Cesium atom:
1 second = 9,192,631,770 oscillations
(303) 499-7111: http://tf.nist.gov/
CC:BY-SAtacoekkel(flickr)http:/
/creativecommons.org/licenses/by-s
a/2.0/deed.en
GETARAN ALAMI
http://tf.nist.gov/http://tf.nist.gov/http://tf.nist.gov/http://tf.nist.gov/ -
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Pola Gerak Harmonik
Ilustrasi pola gerak getaran selaras(harmonik) sederhana.
Karena alasan penjabaran
(deksripsi) matematis, dua ilustrasi
bagian atas tidak dibahas.
Hanya gerak dengan pola sinusoidal(sin atau cos) saja yang dibahas
apa perbedaan pola gerak sinus
dan cosinus?
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Deskripsi Fisis Umum GHS: Frekuensi (f )Periode (T )
The FREQUENCYof a wave is the inverse of the PERIOD.That means that the frequency is the #cycles per sec.
The commonly used unit is HERTZ(HZ).
Tf
fT
Hzs
ccycfFrequency
scycsTPeriod
11
5.05.0sec5.3
75.1
seconds
cycles
275.1
5.3cycles
seconds
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Model Getaran dengan pola GHS: sistem pegas berbeban
An objects maximum
displacement from its
equilibrium position is called the
Amplitude (A) of the motion.
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2cos
tx t A
T
We need a position function to
describe the motion above.
Model Getaran GHS: penjabaran fisis pola ke-berulang-an
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2cos tx t AT
cos 2x t A ft
cosx t A t
1T
f
2
T
x(t) to symbolize positionas a function of time
A =xmax =xmin
when t = T,
cos(2) = cos(0)
x(t) =A
Model Getaran GHS: besaran simpangan (x)
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sinv t A t
cosx t A t d x tv t
dt
In this context we will call
omega Angular Frequency
What is the physical
meaning of the product
(A)?
maxv A
The maximum speed
of an oscillation!
Model Getaran GHS: besaran kecepatan (v) ~ percepatan (a)
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When collecting and modeling data of SHM your
mathematical model had a value as shown below:
x(t) Acost
x(t) Acos tC What if your clock didnt start at x=A or x=-A?
This value represents our initial conditions.
We call it the phase angle:
x(t) Acos t
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The velocity is 90o
out of phase withthe displacement
The acceleration is
180oout of phasewith thedisplacement
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(sin )cos
(cos )sin
axa ax
x
axa ax
x
Review: FUNGSI SINUS
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A
TEquil. point
f=1/T
Review: FUNGSI SINUS(tidak semua gerak bolak-balik merupakan fungsi sinus yang mulus)
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It is aperiodic motion.
AND
It has arestoringforce thatacts to
restore the oscillator to equilibrium.
The restoring force is given by:
Hookes Law F=-kx
x is the displacement fromequilibrium and kis the force
constant (spring constant).
The period of SHM oscillator does
not depend on the amplitude.
Persamaan GHS: sistem pegas berbeban
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Here is what we want to do: DERIVE AN
EXPRESSION THAT DEFINES THE
DISPLACEMENT FROM EQUILIBRIUM OF THESPRING IN TERMS OF TIME.
0)(
2
2
2
xm
k
dt
xd
dt
xdmkx
dt
xd
amakx
maFkxF Netspring
WHAT DOES THIS MEAN? THE SECOND DERIVATIVE OF A FUNCTION
THAT IS ADDED TO A CONSTANT TIMES ITSELF IS EQUAL TO ZERO.
What kind of function will ALWAYS do this?
Persamaan GHS: sistem pegas berbeban: hukum HOOKE
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Since all springs exhibit properties
of circle motion we can use theseexpressions to derive the formula
for the period of a spring.
Besaran Fisis: sistem pegas berbeban
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apa dimensi dari T?
Besaran Fisis: sistem pegas berbeban: periode ~ frekuensi
PERHATIKAN
- Tatau ftidak bergantung pada nilai g- besaran (nilai) kmenggambarkan keras/lemahnya
lenturan pegas
- periode mengecil untuk pegas yang keras (tidak
mudah lentur) nilai kyang besar
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For springs in series:
1/keff= 1/k1+ 1/k2
For springs in
parallel:
keff= k1+ k2
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kis the slope of a
F versusx-graph
Besaran Fisis: sistem pegas berbeban: menentukan nilai k
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Persamaan GHS:Ayunan Matematis (Pendulum)
What length pendulum will have a period of exactly 1s?
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What length pendulum will have a period of exactly 1s?
g
L
T 2 L
g
g T
2
2
L
L9.8m/s2 1s
2
2
0.248m
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A physical pendulum is an oscillating body
that rotates according to the location of itscenter of mass rather than a simple
pendulum where all the mass is located at
the end of a light string.
oscillates about a fixed axis that doesnot pass through its center of mass,
and
the object cannot be approximated as
a point mass,
Persamaan GHS: Pendulum Fisis
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mgd
IT
TI
mgd
Imgd
ifImgd
LdIdmg
IFr
pendulumphysical
2
2,
0)(
sin,
2,sin
sin
It is im por tant to u nders tand
that d is the lever arm
distance or the distance from
the COM posi t ion to the point of
rotat ion.It is also the same d in
the Parallel Axes theorem.
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ExampleA spring is hanging from the ceiling. You know that if you
elongate the spring by 3.0 meters, it will take 330 N of
force to hold it at that position: The spring is then hungand a 5.0-kg mass is attached. The system is allowed toreach equilibrium; then displaced an additional 1.5 metersand released. Calculate the:
kkkxFs )3)((330Spring Constant
Angular frequency 5
1102mk
mk
110 N/m
4.7 rad/s
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29
A uniform rod of mass M and length
L is pivoted about one end andoscillates in a vertical plane.
Find the period of oscillation if the
amplitude of the motion is small.
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Example
Position of mass at maximum velocity
Maximum acceleration of the mass
Position of mass at maximum acceleration
At the equilibrium position
)5.1()7.4( 22Aa 33.135 m/s/s
At maximum amplitude, 1.5 m
A spring is hanging from the ceiling. You know that if you
elongate the spring by 3.0 meters, it will take 330 N of
force to hold it at that position: The spring is then hung
and a 5.0-kg mass is attached. The system is allowed to
reach equilibrium; then displaced an additional 1.5
meters and released. Calculate the:
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b is a constant called
the damping coefficient
Persamaan Gerak Harmonis tidak Sederhana:Ayunan Teredam (damped oscillations)
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is called the natural frequency
CC: BY murdoch666 (flickr) http://creativecommons.org/licenses/by/2.0/deed.en
A slowly changing
line that provides a
border to a rapid
oscillation is calledthe envelopeof the
oscillations.
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Damped Oscillation (oscillation with friction)
The friction reduces the mechanical energy of the system as time
passes, and the motion is said to be damped.
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DampedOscillations
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Exercises
Each:M/2, R
k
stretched by x
and then released
cylinders
rolls w/o
slipping
Ra
MRIIfRfrictionfkxfMa
cmcm
2)2/1(,
):(
.)2/3(/
2
2 xx
M
k
RIM
kxa
cm
.2
32
2
k
MT
f
kx