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PHYS16 – Lecture 32
Ch. 15 Oscillations
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Oscillations pre-question
• Is a ouncin! all an e"a#ple o$si#ple har#onic #otion%
&' Yes
(' )o
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Oscillations pre-question
• *+o ,is are s+in!in! on t+o s+in!s o$ thesa#e hei!ht –
one ,i is a little chuierthan the other. )e!lectin! $rictional
$orces
+hich ,i co#pletes a ac, an $orths+in! in the $astest ti#e%
&' *he chu/ ,i
(' *he s,inn/ ,i
C' *he ,i +ho pushes o0 the !roun the est
' (oth co#plete in the sa#e ti#e
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Outline $or Oscillations
• Simple Harmonic Motion – Position, Velocity,
Acceleration
– Force
– Energy
• esonance an a#pin!
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Oscillations an Perioicotion
http4i#!.t$.co#!!sec!se7888178812787i#!23.
i#ple Har#onic otion
1' &out 9quil.2' Perioic3' Sinusoial
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iscussion4 9"a#ples o$SH%
• ass on a Sprin!
• Penulu#
• Sno+oarer in hal$pipe
• (un!ee :u#per
•
Chil on s+in!• (ole hea oll%
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Si#ple Har#onic otion4Position ;elocit/ &cceleration
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Si#ple Har#onic otion
T
t A x
π ω
ω
2
)sin(
=
=
9quiliriu# Point
http4+++.!ailru/.co#Picture
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iscussion4 Phase
• Your oo, sa/s that isplace#ent isin ter#s o$ cosine an I
:ust sai thatit is in ter#s o$ sine% =ho is ri!ht%
)cos()90sin(
)sin(
t At A x
t A x
ω ω
φ ω
=+=
+=
*here is also a phase ter# >?' that let@s /ou set the
initial conition.I$ the oscillation starts at & it is a sine
+ith a ?A8 e!rees or a cosine+ith a ?A8 e!rees.
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SH Position ;elocit/ &cceleration
4+++.tutorne"t.co#s/ste#BlesuChapterD2811-3.!i$
)sin(
)cos(
)sin(
2 t Aa
t Av
t A x
ω ω
ω ω
ω
−=
=
=
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iscussion
• =hat is the #a" spee an +henoes it occur%
9quiliriu# Point
/2at t 0
0at tmax
π
ω
==
==
v
Av
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9"a#ple Euestion
• &n o:ect uner!oes si#ple har#onic#otion. I$ the a#plitue
an perio areoule the o:ect@s #a" spee is4
&' Euaruple
(' oule
C' Fnchan!e' HalGe
9' Euartere
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Si#ple Har#onic otion4estorin! orce
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estorin! orce
• orce that al+a/s points ac, to theequiliriu# position –
9"a#ple A sprin!
, is :ust a constant – $or a sprin! it is the sprin!constant
xkx F ˆ−=
+++.cs.+ri!ht.eu:slaterS*COutreach=esitei#a!es!i$sprin!7#ass7ia.!i$
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estorin! orce – Sprin!
( ) ( )
m
k f
m
k
xmkx
t Amt Ak
xkx F
π ω
ω
ω ω ω
2
1 ,
)sin()sin(dt
dmma
2
2
2
2
==
−=−
−=−
==−=
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iscussion4 Perio
• & loc, on a sprin! has a perio o$ *.=hat is the perio
i$4
&' the #ass is oule%
(' , is quaruple%
C' & is oule%
T 2
T
2
1
T
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estorin! orce - Penulu#
• =hat is the perio o$ a penulu#%
uploa.+i,i#eia.or!+i,ipeiaenthu#aaPenulu#.pn!388p"-Penulu#.pn!
L
g
smallfor,
)sin(
=
=
−=−=
ω
θ
θ
L smg ks
mg ks F
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Si#ple Har#onic otion49ner!/
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9ner!/ in SH
( ) ( )2
22222
22
2
1
)(cos2
1
)(sin2
1
21
21
kA E
t Ak t Am E
kxmv E
=
+=
+=
ω ω ω
+++.$arra!uttn.co#science#illi!an&PPh/sSHOGer7Blesi#a!e822.:p!
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ain Points - SH
• oGe#ent
•
estorin! orce creates oscillation
•
9ner!/ is epenent on a#plitue
)sin( t A x ω =
2
2
dt
xd mkx F =−=
2
2
1kA E =
