Cong Thuc Vat Ly 12co Bo Sung

5/19/2018 Cong Thuc Vat Ly 12co Bo Sung

1/15

TI LIU HC TP MN VT L LP 12

TM TT

(CHNG TRNH CHUN)

1


2/15

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 !


3/15

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


4/15

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


5/15

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


6/15

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


7/15

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


8/15

+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


9/15

!! )( 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


10/15

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


11/15

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


12/15

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= (`)


13/15

| 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


14/15

+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 = +

14


15/15

Cong Thuc Vat Ly 12co Bo Sung

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