cong thuc vat ly 12co bo sung
TRANSCRIPT
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TI LIU HC TP MN VT L LP 12
TM TT
(CHNG TRNH CHUN)
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NGUYN HIN TR GV. THPT V TH SU
CNG THC VT L 12
DAO NG V SNG CI. DAO NG IU HA
Chn gc ta ti v tr cn bng:
Phng trnh dao ng:
os( )x Ac t = +
Phng trnh vn tc:
sin( )v A t = +
Phng trnh gia tc:
! !os( )a Ac t x = + =
": #i dao ng (c$% $)
&: 'in dao ng (c$% $)
: Pha ban * ( rad)
: +n s g,c (rad-s) )( +t : Pha dao ng (rad)
C.c gi. tr
c/c i
H thc c lp: !
!
!!
vxA +=
! !v A x=
0T!" VTC#: " 1 2% v$a"1 A % a1 2
0T!" $"%&: "$a"1 &% v 1 2% a$a" 1
A!
0T'( )* +,-& $/&0 +,& 1 (0-/:
3A
vT
=
0 L"%& 03 45 607:
v s4$ 5ha!
hn "6
a s4$ 5ha! hn v6 a ng7c 5ha
v4i "
II. CON L8C L 9O
Tn s gc:m
k=
!mk= 6 f !=
Chu k:!=T
k
mT !=
Tn s:T
f 8=
m
kf
!
8=
9* $ 1$8 0 $! !
!
!
8
!TTT +=
9* $ 1$8 ; $! !
!
!
8
!TTT =
9* trong tht ?@ "o:
8 8 ! !A A Ak l k l k l = =
2
"$a"1 &v$a"1 A ( +iB+C')
1 !
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hD5 ?@ "o:
0 9* E8ni ti5 E!:8 !
8 8 8
k k k= +
!
!
!
8
!
TTT +=
0 9* E8song song E!: 8 !k k k= +
! ! !8 !
8 8 8
T T T= +
L h!"n# $%nh &'( )*n#)+,u h-':
Phng trnh c, dng:cos( )x A t = +
0 Tm :
m
k= %
!
T
= %
f != % F0 Tm A:
!
!!!
vxA += % l1!&% v$a" 1
A %F
0 Tm :Chn t 1 2 ?Gc vt H*a vtr "2
2 osx Ac =
2cos cosxA
= =
= Bt CI thJochiK* (;)
= Bt CI thJochiK* (0)
Nn# /!0n# &'( )*n# )+,u
h-'1
*& &:&:
! 1! !
!sin ( )! !
mv kAt = +
T0; &:&:
t! 1! !
!cos ( )! !
kx kAt = +
C< &:&:
!1 ! 0 t! 1 hng s
!1!
!
kA1
! !
!
m A1
!
$a"
!
mv
C(n /23 /- 4( $%5( $h6n# )7n#:
i ?2 : ChiK* dLi t/ nhin cMa ?@ "o
l : I dNn cMa ?@ "o Ehi vt OB+C'
?b: ChiK* dLi cMa ?@ "o Ehi vt OB+C'
lll" +=
2
8h+ 9$ : VTC;1 h1 P
mglk =
l
g
m
k
==
Chu k 3
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Ch#$u %# c&c t#(u
(Qhi vt O v tr cao nhRt) ?$in 1 ?b;&
!$in$a" ll
A
=
!
$in$a" lll"+
=
L=( )>& 0?" (@7 B " )* :
h1 E( l 0 ")L=3 )>n h?+ 3=3 )@+:
h$a"1 E( l 0 &)L=3 )>n h?+ 3=3 $+Au:
h$in1 E( l ; &) n* l S &
h$in1 2 n* l & L=( E 45:
#L ?/c tTng h75 t.c dUng ?n vt
( c, "* h4ng a vt vK B+C')
I ?4n kx)hp =
*&c h+# ph,c c&c '#:kA)hp =
LF- T,& (( (& +0J( 45 =(4> &:& FK& +0/ A l ( ) Q.
III. CON L8C RN
Tn s #B3:l
g=
Chu k:g
lT != ?($)%
g($-s!)
Tn s:l
gf
!
8= (VW)
Ph!"n# $%nh &'( )*n#:
Th-. cung lch:
2cos( )s s t = +
Th-. gc lch:
2cos( )t = +
B4i ls=
l ?L chiK* dLi dX trJo ($)6
22 %s ?L g,c ?=ch % c*ng ?=ch Ehivt O bin (rad)A
0 CYng thZc ?in h=:!
! !
2 !
v/ s
= +
BL ! !2
v / s=
VS& +'(Qhi dX trJo ?=ch g,c bRt E:
)cos(cos! 2= glv
Qhi vt H*a B+C':
)cos8(! 2= glv
Qhi vt O bin: v 1 2
L=( (:& Qhi vt O g,c ?=ch bRt E:
T 1 )cos!cos[( 2mg
Qhi vt H*a B+C'
T 1 )cos![( 2mg Qhi vt O bin: T 1
2cosmg
0h# 282 C, th\ d]ng
8; cos 2 1!!
sin!!
22!
Tmax 1 )8( !2+mg 6
4
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Tmin1 )!
8(!
2mg
Nn# /!0n# &'( )*n#1
! 1 ! 0 t! 1 hs!
2 2
8(8 cos )
!! mgl mgl =
Ch* E t^ng haX gi_$ thJo `:
! 8
8
A822`T T
T
ChiK* dLi t^ng haX gi_$ thJo `:
! 8
8
A822`l l
l
ia tc t^ng haX gi_$ thJo `:
! 8
8
A822`g g
g
IV. TWNG HXP DAO NGDt ! dao ng iK* h@a c]ng
5hng c]ng tn s:
8 8 8cos( )x A t = +
vL ! ! !cos( )x A t = +
* 3(0 607: 8! =
Phng trnh dao ng tTng h75 c,dng:os( )x Ac t = +
cos(! 8!!8!
!
!
8 ++= AAAAA
!!88
!!88
coscos
sinsin
AA
AAtg
+
+=
N1u 2 a. ng c3ng pha:
k!= 8 !A A A= +
N1u 2 a. ng ng45c pha:
)8!( += k
8 !A A A= T6ng 7u8t
8 ! 8 !A A A A A +
V. YZNG CR HC
Y& 1 &-?&
Dt s,ng ti ng*n c, bi\* thZc
os.u Ac t =
'i\* thZc s,ng ti c.ch Eho_ngd:
!os( )9
u Ac t
=
04;c sng:Tv
f
vA==
0 $n sng:s
vt
=
? lch pha g#@a 2 #(m t=nph4Bng t=u>$n sng c8ch nhau kh.Dng :
!
=N1u 2 a. ng c3ng pha:
k!= k=
N1u 2 a. ng ng45c pha:
)8!( += k
8( )
!
k = +
5
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G"7 +07 [&
Dt s,ng ti ! ng*n e8 vL e! ?L !s,ng Et h75 c, bi\* thZc:
osu Ac t =
0 Dt i\$ c.ch ng*n & $tEho_ng d8% c.ch ng*n ' $t Eho_ngd!
0 'i\* thZc s,ng ti do e8tr*XKnt4i:
88
!os( )
u Ac t
=
0 'i\* thZc s,ng ti do e!tr*XKnt4i:
!!
!os( )
u Ac t
=
'i\* thZc s,ng tTng h75 ti :
*1 *80 *!
#n :
! 8! cos A A A =
Eha "an u:
8 !( )
+=
C&c '# g#a. th.a:
&$a"1 !& k = 8! C&c t#(u g#a. th.a:
&$in 1 2
)!
8(8! += k
+r
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M!(0 (0d ( e
1 2% -e " (f& 607
JHI J 22 = 6 JIJ A=
M!(0 (0d ( (-*& (g L:
CDm kh8ng *K* =
1!
-L&07&0 607 0
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+Tng trO:
!! )()( C* KK=JK ++=
I ?=ch 5ha cMa * so v4i i:
=JKKtg C*
+=
CYng s*Rt $ch:
P1(0r)A!
V= s cYng s*Rt $ch:
K
=J+=cos
G0E6 +h )"3&:
Qhi CghD5 vLo Cto thLnh Cb0 9* Cb C: CghD5 nt C
888
CCC"+=
0 9* Cb S C: C ghD5 -- v4i C
Cb1 C 0 C
#>" +& (=( +,
Th'E )+ R )A P'41
CYng s*Rt P 1 !1
J
KK
J
I
KKJ
IJ
*C*
!
!!
!
()(A
+
=+
I\ P$a"
$in
!)(
+
J
KKJ C*
J
KKJ C*
!)( =
C* KKJ =
J
I
!
!
$a" =
Th'E )+ L )A UL'4:
** KI A= 1
!! )(
A
C*
*
KKJ
KI
+1
>
I
KK
KKJ
I
*
C
*
C
=
++ 88
A!8
)(!
!!
I\ j#$a"th X$in X 1 2
C
C
*K
KJK
!!+
=
!!$a" C* KJJ
II +=
Th'E )+ C )A UC'41
T4Bng t&:*
*
CK
KJK
!!+
= 6
!!
$a" *C KJJ
II +=
II. LIjN H GIkA ClC INlP
0 Vai * c, i=n .5 hi=* dUngj
0 Vai * # c, i=n .5 hi=* dUngj#
0 Vai * C c, i=n .5 hi=* dUngjC"3& 6 0"3- h& 2 )m- !(0
8
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!! )( C*J IIII +=
? lch pha cRa u s. v;# #:
J
C*
I
IItg
=
H s cPng suQt m'ch:
I
IJ=cos
n0" (-*& ( )"3& +, +,&:
!! )()( C*=J IIIII ++=
C-*& (:!!
*= III +=
=
*
I
Itg = 6
=
I
I=cos
III. YoN 9UpT V TeUbNToI IN NqNG
E h$ )+Fn 4('E 3h+,u Jh'1
Tn s: Af n p=
v4i 5: e cp5 c/c cMa na$ch$A
n: e v@ng H*aX trong 8s
/uQt #n ng cDm ng:
2cos- S t=
c hnh sao:
[ pI I= vL p =
0 >c hnh ta$ gi.c:
pI I= vL [ p =
M $";& +0;
i:98% j8% P8: e v@ng% i=n .5 hi=*
dUng% cYng s*Rt O c*n [< (i6
9!% j!% P!: e v@ng% i=n .5 hi=*dUng% cYng s*Rt O c*n +0J (i6
8888 cosHIE = 6
!!!! cosIE =
H#u suQt cRa m8> "#1n th1:
88
! =E
EH (`)
9'ch th cQp khPng tD#:
!
8
!
8
I
I
N
Nk ==
9'ch th cQp c tD#: UlV t4MngW
8
!
!
8
!
8
I
I
N
Nk ===
T,-5& +g" )"3& &:&:
? g#Dm th1 t=n X> Yn:
JI=
CPng suQt ha. phV t=n 4Zng
X> tD# #n:
!
!! A
I
EJJE ==
B4i d: i=n trO tTng cng trn
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8
8
8
!
E
EE
E
EH
== `A B4i:
8E: CYng s*Rt tr*XKn i
!E: CYng s*Rt nhn 7c ni ti*thU
E : CYng s*Rt hao 5h
DAO NG V SNG INT
Tn s gc:*C
8=
Chu k =#ng: *CT !=
Tn s =#ng :
*CTf
!
88==
4;c sng #n t:
A A!
c
c T c *C f = = =
B4i Cs 1 [A82q $-s: Bn tc .nhs.ng
N:& FK& !(0 7 )*&
N[ng l45ng #n t=4Zng:
!!8 8 8
! ! !C
7! Cu 7u
C
= = =
N[ng l45ng #n t=4Zng c&c'#:
!! 2
$a" 2 2 2
8 8 8
! ! !C
\! CI \ I
C= =
N[ng l45ng t t=4Zng:
!8
!*! *#=
N[ng l45ng t t=4Zng c&c '#:
!
$a" 2
8
!*! *=
N:& FK& )"3& +_: 1 C0 #
! !
!! !
8 8
! !
8 8 8 8
! ! ! !
! Cu *#
77u *# *#
C
= +
= + = +
!
$a" $a" 2
!!2
2 2 2
8
!
8 8 8
! ! !
C *! ! ! CI
\\ I *
C
= = =
= = =
Nn# /!0n# )+Fn $%!Kn# 9>
nn# /!0n# $ $%!Kn# M+n $h+On)+,u h-' 9+ $n s #Q )+ 3
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0 : '4c s,ng cMa .nh s.ng Echthch
0 ": Qho_ng c.ch tf v tr vn ang"Dt t4i vn s.ng tr*ng t$
00h.Dng vXn:aL# =
0
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0 : '4c s,ng .nh s.ng Echthch
0 2 : '4c s,ng gi4i hn cMa Ei$
?oi
"5- "3& )\ g ,7 0"3& +FK&
u-7& )"3&: 2
N[ng l45ng cRa phPtPn 8nh s8ng:
hchf == (y)
CPng th.8t cRa -l-ct=.n :
2
hcA = (y)
Eh4Bng t=nh Anhxtanh:
$a"2!A +=
B4i 2$a"1!
$a"2!
8mv
C( 0w& [':
h 1 x%x!uA82;[3yAs6 c 1 [A82q$-s%
J 1 8%xA82;8zC 6 $J1 z%8A82;[8Eg
C4Zng _ng 7uang #n "D.h_a:
t
-n -"h
A= (&)
CPng suQt ngu+n "c x':
t
nE
pA
= ()
H#u suQt l45ng t :p
-
nnH= (`)
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| 1 $c!A
I hUt Ehi cMa ht nhn :
$ 1 k$50 (& } k)$n} $hnA
9^ng ?7ng ?in Et: ?E 1$Ac!A
9^ng ?7ng ?in Et ring:?Er 1
A
!lk
P0& ! :
b 0 Vt 5h,ng "
]^# +: #L ch* E b.n rNt: +h
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+rong 5h_n Zng ht nhn:
88
A
K 80!
!
AK !
[
[
AK [0
3
3
AK
3A
/ nuclPn v% s #n tVch 45c "D.t.%n:
&80&!1 &[0 &3 vL k80 k!1 k[0k3
N[ng l45ng $X' %' h.c $hu 9>(t=.ng phDn ng h't nhXn:
1 ($80 $!; $[; $3)c!
1 ($80 $!; $[;$3)Az[8%uJB
1 ($[0 $3; $8; $!)Ac!
1&[?Er[0 &3?Er3; &8?Er8;&!?Er!
[ 3 8 !( )! 0 0 0 0 = +
0 N;- 1~ 2 ~ th 5h_n Zng ht nhn +7 &:&
FK&A
0 N;- 1~ 2 ~
th 5h_n Zng ht nhn +0- &:&FK&A
In v Ehi ?7ng ng*Xn t:8* 1 z[8%u
!
9-1t t4Bng #! !
2mc m c 0 = +
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