l`ivphet mr sxb
ewewnd ewd oia yxtd oi`yk dxew dfe ,zqt`zn zihpiwd dibxp`d xy`k zqt`zn sebd zexidn .`
.'fe '` ,zecewp izya dxew df .l`ivphetd sxbl
dcewpa dxew dfe ,ilniqwn dibxp`d sxbl ewewnd ewd oia yxtddyk zilniqwn sebd zexidn
.a
.'d
.'de,'c,'ba dxew dfe ,zqt`zn l`ivphetd zxfbpyk qt`zn gekd .b
.dpini gekd zilily `idyke ,dl`ny gekd ,ziaeig `id xy`k
.zxfbpd ici lr rawp gekd oeeik
.c
.'dl 'c oiae 'bl '` oia dl`ny gekde ,'fl 'd oiae 'cl 'b oia dpini gekd ,eply dxwna
okl ,)miizy iwlg dqn ick cr( ,l`ivphetd sxbl eweewnd ewd oia yxtdl deey reaixa zexidnd .d
:scd z` jetdl jixv heyt
.xeyw lelqna `ed okle ,seqpi` qepinl e` seqpi`l repl leki `l sebd .e
1
zlhehn ly l`ivphet
okle drepzd oeeikl avip cinz hend ly gekd .hend ly gekde ,caekd gek ,zegek ipy milret sebd lr .`
mgh
.
l`ivphet mr ,oaenk xnyn caekd gek .dcear dyer `l
mcew xgap xy`k ,zieefa zelzk sebd daeb z` `hap .
mgh
xen`k `id zil`ivphetd dibxp`d .a
:lawp dixhnepebixhn .sebd ly dkenp ikd dcewpa zeidl
0d
daeb z` zizexixy dxeva
h = l(1 − cos θ)
U (θ) = mgh = mgl(1 − cos θ)
.b
.gekd oeeik z` mibivn minec`d mivgd .c
θ = 2πn + 1a
.
mbe
θ = 2πna
mb ,(0 l`ivphetd retiy xy`k) lwyn ieeiy zecewp yi .d
zizgza `vnp sebd xy`k zecewpd dl` .zeaivi ode , menipina od (
θ = 2πn)
zekenpd zecewpd
dpeilrd dcewpa `vnp sebd mda miavnd dl` .zeaivi `l ode ,meniqwna od zedeabd zecewpd .lbrnd
.lbrna
ipy oia mi`vnp mixeywd milelqnd .mixeyw `l milelqn ode mixeyw milelqn od rval leki sebd .e
mi`vnp mixeyw `ld milelqnd .aeye jeld zcpcpzn zlhehnd ea avna xaecn .l`ivphetd ly miwit
.oeeik eze`l miaeaiqd lk xy`k zilbrn drepz rvan seb dl` milelqnae ,l`ivphetd ly miwitd lrn
.oeeik dpyn `l la` ,ick jez ui`ne hi`n `edy oaenk
-hetd ly meniqwnl menipind oia z`vnp zllekd zipknd dibxp`d xy`k eygxzi mixeyw miavn .f
,mzxgay qt`d zcewpa miielz zeniqwnde zenipind mbe ,zllekd zipknd dibxp`dy al eniy .l`ivp
:eply dxwna .zepexztd lka ddf zeidl aiig lbrnd zizgza zihpiwd dibxp`d megzy oaenk la`
Umin < K0 + U0 < Umax
U0 = U (0) = 0
Umin = U (0) = 0
Umax = U (π) = 2mgl
0 < K0 < 2mgl
1
xnqne heg
okle drepzl zavip cinz zegiznd epiptly diraa .zegiznde caekd wx md dqnd lr milretd zegekd
h = 0) qt`d daeb z` rawp
dlgzdd zcewpa ( 0
.zipkn dibxp` xeniy yi ,ok m` .dcear dyer dpi` `id
:`id dlgzda dibxp`d .drepzd ly
Ei = Ki + Ui = 0
:daeba `vnp sebd ,
α
zieefa hegdyk
L
h1 = (cos α − 1)
2
:`id seqa zipknd dibxp`d okl
Ef = Kf + Uf =
mv12
L
+ mg (cos α − 1)
2
2
:lawpe ,zxnyp dibxp`d okle zxg` dcear ziyrp `l mcew epxn`y enk
Ei = Ef
0=
mv12
L
+ mg (cos α − 1)
2
2
2
v1 = gL(1 − cos α)
deey zeidl dkixv zil`icxd dve`zd ,dl`yd ly dfd wlga .zegiznd iabl mil`ey `ad sirqa
:l
v2
v2
v2
ar =
=
=2
r
L/2
L
:md il`icxd aikxa zegekd
T + mg cos α
:okle
T + mg cos α = 2m
v2
L
T
v2
= 2 − g cos α = 2g(1 − cos α) − g cos α = g(2 − 3 cos α)
m
L
zegizndyky milawn epgp` o`kn .mcewd wxta ep`vny `hz zieefa zexidnd z` jxca epavd xy`k
.
1
2
deey qepiqewd ,zqt`zn
3