ap simple harmonic motion
TRANSCRIPT
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Simple
Harmonic
Motion
AP Physics C
Mrs. Coyle
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Periodic MotionPeriodic Motion A motion of an object that repeats with a
constant period.
http://www.sccs.swarthmore.edu/users/!/ajb/e"#/lab#/
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SimpleSimpleHarmonicHarmonicMotionMotion
$t is aperiodic motion.A%&
$t has arestoringforce thatacts to restore
the oscillator to e'uilibrium. (he restorin)force is )i*en by:
Hookes Law F=-kx
x is the displacement from e'uilibrium and kis theforce constant +sprin) constant,.
(he period of SHM oscillator does not depend
on the amplitude.
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Simple Harmonic Motion
Simulationshttp://bcs.wiley.com/he-bcs/oos0
action1minina*2bcs$d13442item$d15"#
"6!#72asset$d1###"2resource$d1#8
##
-SHM
-Particle oscillatin) in SHM
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Calculatin) from a 9 *s ;raph is the slope of a 9 *s )raph
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(he acceleration in SHM is not
constant:
Hooke Newton
x
x
F F
kx ma
ka xm
=
=
=
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Acceleration in Simple
Harmonic Motion Acceleration
>et
a1 -8x
2
2
d x ka x
dt m= =
2 k
m =
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Characteristic ?uantities of Simple
Harmonic Motion &isplacement
Amplitude: maimum displacement
9re'uency
Period
f1#/( (1#/f
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SimpleSimpleHarmonicHarmonicMotionMotion Velocity:
@ maimumas it
passes throu)h
e'uilibrium
@ eroas it passes
throu)h the etremepositions in its
oscillation.
cceleration!a=F"m = -kx"m
-maimumat etremepoints
-eroat e'uilibrium
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B'uations of Motion-
&isplacement
1Asin+t+, or 1Acos+t +)
1-Asin+t+, 1-Acos+t+,
=an)ular fre'uency rad/s is the phase constant
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Bample
a, Dhat is the amplitude0
b, Dhat is the period0
c, Dhat total distance does the particle tra*el in
one period0
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Bample
Drite the e'uation of motion for the abo*e oscillator.
Answer:
1-.6sin+Et,
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%ote #$e acceleration is not constant and
t$erefore t$e kinematics e%&ations cannot'e &sed.
#$ere are two options!#.Fse conser*ation of mechanical ener)y to
find * at a )i*en position.
B1 G m*8= G 8 1 constant or8. (ae the first deri(ati(eof +e'uation of
motion, to find (and the second deri(ati(e
to find a.
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Bamples of Motion B'uations
for Simple Harmonic Motion
22
2
( ) cos ( )
sin ( t )
cos( t )
x t A t
dxv A
dt
d x
a Adt
= +
= = +
= = +
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max
2
max
kv A A
mk
a A A
m
= =
= =
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;raphs of
SHM
(he *elocity is 7o
out of phase withthe displacement
(he acceleration is
#!oout of phasewith thedisplacement
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Bample #
t1
x +,1A
v +, 1 1
ama 1 8A
*ma 1 A
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Bample 8
t1
x +,1
v +, 1 vi
1 /8
(he )raph is shiftedone-'uarter cycle to theri)ht compared to the)raph ofx +, 1A
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Period and 9re'uency
22
T
= =
12 , 2
m kTk m
= =
2 k
m
=
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Period of A Sprin) Mass scillator
IIII
(18)m/
m mass
sprin) constant
( does not depend on ) (he period is smaller for a stiffer sprin)
+lar)e *alues of k,.
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Harmonic Motion of a Pendulum
http://www3.interscience.wiley.com:!#/le)acy/colle)e/halliday/5"#386/simulations4e/inde.htm0newwindow1true
Period
III
(18)>/)
>1len)th of strin) ( depends on )
>
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?uestion
$f you had a sprin)-mass system on the
moon would the period be the same or
different than that of this system on the
earth0
Dhat if it were a pendulum system0