H„»â€  TH„»¯NG TO£â‚¬N...

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  • 1

    H THNG TON B CNG THC

    VT L 12 T A-Z

    sin

    3

    4

    6

    6

    4

    3

    2

    3

    2

    4

    3

    6

    5

    6

    5

    2

    3

    2

    4

    3

    2

    3A

    2

    2A

    2

    1A

    22A

    2

    1A

    23A

    22A-

    2

    1A-

    23A-

    2

    3A

    2

    2A-

    2

    1A- A

    0 -A

    0

    W=3Wt

    W=3Wt

    W=Wt

    Wt=3W

    W=Wt

    2/2vv max

    23vv max

    2/vv max2/vv max

    22 vv max

    v < 0

    23vv max

    x

    V > 0

    Wt=3W

    +

    cos

  • 2

    CNG THC VT L 12

    CHNG I : DAO NG

    I. 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:

    2 2os( )a Ac t x

    + x: Li dao ng (cm, m)

    + A: Bin dao ng (cm, m)

    + : Pha ban u ( rad)

    + : Tn s gc (rad/s)

    + )( t : Pha dao ng (rad)

    H thc c lp: 2

    222

    vxA

    2 2v A x

    +Ti VTCB: x =0, vmax = A , a = 0

    +Ti bin: xmax = A, v = 0, amax = A2

    +Tc trung bnh trong 1 chu k:

    4A

    vT

    + Lin h v pha:

    v sm pha 2

    hn x;

    a sm pha 2

    hn v; a ngc pha vi

    x

    II. CON LC L XO:

    Tn s gc: m

    k

    2mk , f 2

    Chu k:

    2T

    k

    mT 2 ,

    Tn s: T

    f1

    m

    kf

    2

    1 ,

    Nu m =m1 + m2 2

    2

    2

    1

    2 TTT

    Nu m =m1 - m2 2

    2

    2

    1

    2 TTT

    Nu trong thi gian t vt thc hin

    c N dao ng:

    Chu k N

    tT Tn s Nf

    t

    Ct l xo:

    1 1 2 2. . .k l k l k l

    Ghp l xo:

    + Nu k1 ni tip k2:

    1 2

    1 1 1

    k k k

    xmax = A

    vmax = A ( Ti VTCB)

    amax = A2 ( Ti bin)

  • 3

    2

    2

    2

    1

    2 TTT

    + Nu k1 song song k2: 1 2k k k

    2 2 2

    1 2

    1 1 1

    T T T

    Lp phng trnh dao ng iu ha:

    Phng trnh c dng:

    cos( )x A t

    + Tm A:

    2

    222

    vxA , l =2A, vmax = A ,

    + Tm :

    2T , f 2 ,

    m

    k

    + Tm : Chn t = 0 lc vt qua v tr x0

    0 osx Ac

    0cos cosx

    A

    Vt C theo chiu (-)

    Vt C theo chiu (+)

    Nng lng dao ng iu ha:

    ng nng:

    dW = 2 2 21 1 sin ( )

    2 2mv kA t

    Th nng:

    tW = 2 2 21 1 cos ( )

    2 2kx kA t

    C nng:

    W = dW + tW = hs

    W = 2

    2

    1kA = 22

    2

    1Am = hs

    Con lc l xo treo thng ng:

    Gi l0 : Chiu di t nhin ca l xo

    l : dn ca l xo khi vt VTCB

    lb : Chiu di ca l xo khi vt

    VTCB

    lllb 0

    Khi vt VTCB:

    Fh = P

    mglk

    l

    g

    m

    k

    Chu k ca con lc

    g

    l

    k

    mT

    22

    Chiu di ca l xo li x: l = lb + x

    Chiu di cc i

    (Khi vt v tr thp nht) lmax = lb +

    A

    Chiu di cc tiu

    (Khi vt v tr cao nht) lmin = lb - A

    2

    minmax llA

    ;

    2

    minmax lllb

    lk

    0l

    m bl

    m

  • 4

    Lc n hi ca l xo li x:

    Fh = k( l + x)

    Lc n hi cc i:

    Fhmax = k( l + A)

    Lc n hi cc tiu:

    Fhmin = k( l - A) nu l > A

    Fhmin = 0 nu l A

    Lc hi phc:

    L lc tng hp tc dng ln vt

    ( c xu hng a vt v VTCB)

    ln kxFhp

    Lc hi phc cc i: kAFhp

    Lu : Trong cc cng thc v lc v

    nng lng th A, x, l c n v l (m).

    III. CON LC N

    Tn s gc: l

    g

    Chu k:g

    lT 2 l(m), g(m/s2)

    Tn s: l

    gf

    2

    1 (Hz)

    Phng trnh dao ng:

    Theo cung lch: 0cos( )s s t

    Theo gc lch: 0cos( )t

    Vi ls

    l l chiu di dy treo (m)

    00 , s l gc lch , cung lch khi vt

    bin

    + Cng thc lin h:

    22 2

    0 2

    vS s

    V 2 2

    0v S s

    Vn tc:

    Khi dy treo lch gc bt k:

    )cos(cos2 0 glv

    Khi vt qua VTCB:

    )cos1(2 0 glv

    Khi vt bin: v = 0

    Lc cng dy:

    Khi vt gc lch bt k:

    = )cos2cos3( 0 mg

    Khi vt qua VTCB

    = )cos23( 0mg

    Khi vt bin:

    = 0cosmg

    Khi 010 C th dng

    1- cos 0 = 22

    sin22

    002

    = )1( 20mg ;

    = )2

    1(2

    0mg

    Nng lng dao ng:

    W = dW + tW = hs

    2

    0 0

    1(1 cos )

    2W mgl mgl

  • 5

    Chu k tng hay gim theo %:

    2 1

    1

    .100%T T

    T

    Chiu di tng hay gim theo %:

    2 1

    1

    .100%l l

    l

    Gia tc tng hay gim theo %:

    2 1

    1

    .100%g g

    g

    IV. TNG HP DAO NG

    Xt 2 dao ng iu ha cng phng

    cng tn s:

    1 1 1cos( )x A t

    v 2 2 2cos( )x A t

    lch pha: 12

    Phng trnh dao ng tng hp c

    dng: os( )x Ac t

    Vi:

    )cos(2 12212

    2

    2

    1 AAAAA

    2211

    2211

    coscos

    sinsin

    AA

    AAtg

    Nu 2 dao ng cng pha:

    k2

    Nu 2 dao ng ngc pha:

    )12( k

    + Nu 1 2A A th 2 2 2

    1 2A A A

    + Nu A tng l ng cho hnh thoi 0120 1 2A A A

    + Nu A tng l hnh thoi 060

    1 23 3A A A

    CHNG II: SNG C HC

    Sng do 1 ngun

    Xt sng ti ngun O c biu thc

    osou Ac t

    Biu thc sng ti M cch O khong d:

    2

    os( )Md

    u Ac t

    Vi : 2 f

    + Bc sng: Tvf

    v.

    + Vn tc truyn sng: svt

    lch pha gia 2 im trn phng

    truyn sng cch nhau 1 khong d:

    d2

    Nu 2 dao ng cng pha:

    k2 d k

    Nu 2 dao ng ngc pha:

    )12( k 1

    ( )2

    d k

  • 6

    Giao thoa sng:

    Xt sng ti 2 ngun A v B l 2 sng

    kt hp c biu thc: osu Ac t

    + Xt im M cch ngun A mt

    khong d1, cch ngun B mt khong d2

    + Biu thc sng ti M do A truyn ti:

    112

    os( )d

    u Ac t

    + Biu thc sng ti M do B truyn ti:

    222

    os( )d

    u Ac t

    Biu thc sng tng hp ti M :

    uM = u1 + u2

    Bin : 2 12 cos .

    d dA A

    + Cc i giao thoa:

    Amax = 2A kdd 12

    + Cc tiu giao thoa:

    Amin = 0 )2

    1(12 kdd

    tm s cc i giao thoa:

    k2 kdd 12

    v d1 + d2 = S1S2

    tm s cc tiu giao thoa:

    )12( k

    )2

    1(12 kdd

    v d1 + d2 = S1S2

    Trng hp sng pht ra t hai

    ngun lch pha nhau = 2 - 1 th s

    cc i v cc tiu trn on thng S1S2

    l s cc gi tr ca k ( z) tnh theo

    cng thc:

    Cc i:

    1 22

    S S

    < k < 1 2

    2

    S S

    .

    Cc tiu:

    11 22 2

    S S

    < k <

    11 22 2

    S S

    .

    Sng dng:

    Gi l l chiu di ca dy, k s b sng:

    + Nu u A c nh, B c nh:

    2

    l k

    + Nu u A c nh, B t do:

    1

    ( )2 2

    l k

    CHNG 3 :DONG IEN XOAY CHIEU

    I. I CNG IN XOAY CHIU

    Biu thc cng dng in v in

    p

    0cos( )ii I t

    v 0 cos( )uu U t

    lch pha ca u so vi i: u i

    + > 0: u nhanh pha hn i

    + < 0: u chm pha hn i

    + = 0: u, i cng pha

  • 7

    Mch ch c R:

    = 0, uR , i cng pha

    RIU R 00 ; RIUR .

    Mch ch c cun cm L:

    Cm khng LZL

    =2

    uL nhanh pha hn i :

    2

    LL ZIU .00 ; LL ZIU .

    Mch ch c t in C:

    Dung khng C

    ZC

    1

    = -2

    uC chm pha hn i :

    2

    CC ZIU .00 ; CC ZIU .

    on mch R, L ,C ni tip:

    Tng tr: 22 )( CL ZZRZ

    lch pha ca u so vi i:

    R

    ZZtg CL

    nh lut ohm :

    ZIU .00 ; ZIU .

    Lu : S ch Ampe k: 0

    2

    II

    S ch vn k: 2

    0UU

    Cng sut mch RLC:

    cosUIP ; P=RI2 = UR.I

    H s cng sut mch: Z

    Rcos

    Mch RLC cng hng:

    Thay i L, C, n khi CL ZZ

    Khi Zmin = R min

    maxZ

    UI

    R

    UIRP

    22

    maxmax .

    iu kin cng hng:

    + Cng sut mch cc i

    + H s cng sut cc i

    + Cd, s ch ampe k cc i

    + u, i cng pha

    Cun dy c in tr trong r:

    Tng tr cun dy:

    22

    Ld ZrZ

    lch pha gia ud v i:

    r

    Ztg Ld

    Cng sut cun dy: 2.IrPd

    H s cng sut cun dy:

    d

    dZ

    rcos

    Mch RLC khi cun dyc in tr r:

    Tng tr:

    22 )()( CL ZZrRZ

    lch pha ca u so vi i:

  • 8

    rR

    ZZtg CL

    Cng sut mch: P=(R+r).I2

    H s cng sut mch:

    Z

    rR cos

    Ghp t in: Khi C ghp vo C to

    thnh Cb

    + Nu Cb < C:C ghp nt C

    '

    111

    CCCb

    + Nu Cb > C: C ghp // vi C

    Cb = C + C

    Bi ton cc tr:

    Thay i R Pmax:

    Cng sut P=RI2 =

    R

    ZZR

    U

    ZZR

    UR

    CLCL

    2

    2

    22

    2

    )()(.

    Pmax

    min

    2)(

    R

    ZZR CL

    R

    ZZR CL

    2)(

    CL ZZR R

    UP

    2

    2

    max