Aula_34_-_Oscilador_LC_Oscilador_RLC_e_Fasores_17.12.2012_

Prévia do material em texto

1f.12.1012
Aulõ1 rassJd<:1:
.f CtV + L:
ilvL ~ í1VLo 005 Wt
•• ~ (!JVLO )SCh wt
WL
-p" t"'~LO)SE" 2wi
r-p::::o
.
X ~ W l ~ Á- -=> IJ.VLV'Wl$L rV'l\S --='-'----
XL
TvDJhS fovvn ~ dQV;
1( CN + C :
IJ.Vc: ":: !J.Vt-O Cos w+
Á-- => - wqo Sen wt
p~(-,lO~Vw)se" 2wi
r-=o
Xc. == ~ ~ ~rW\s -= 4VC,rms
wc Xc
1. C,r eu/to LC sem G'evéI do V-
;""\Qlva
-QT C Me;; /J.I/L
'--_._.-.JJ Vb ~-t(Võl-Vb)
-I- ~~--.::...~ _.
;(...
Se LlVc~ DVL ) pela leI d;;)s Wl~-
Ihcts:
uh + 14- ~ O (1)
L d+/ ~
- 1J.VL. + !JVc
L" ~ J sUbs1 eW' (1) :
dt"l- ~
II
<H> Lq(-t) + ~ ~ O (2)
I C
L
II
m X({) + K x: (f) ~O (3J
( FR:: m~ =. - KX))(0 x
(::o)
A h a 1, sêlVldo a 5 e~u I Yê) Ié' V1ela s (ti) I Condu / VVlOS que..
L---? (br-ves ~OVl de ~ 1n;v- CI a de. Um C.iVcuibJ
(se. o~e ~s VóWIêl 9SÉ'S na CovYcYl-te) a C
A soluS;o CoVlhcclda (fl~'C~ 7) ri ól eq.dlleveVlGlê11 (3) e/:
1 )(-= A CoS lw+- 'l.) ) LJ ~ Ir j (5)
f"m·f~",-to) ::.Jpl,cCJl1do ~s equ1v"le".,Clêls C~) na sofucJiO (5).
r ~ ~ A Cos (IA)f-';))) W" {!1 r ((,)
Ca v~a Oscda",fc VI o ca pa c,for
r@Yél ~VI con.+"n mOS ;;j Covro1fe.) b~sfCJ cten VólVVVlOS (b):
\ ,.L ~ - LJ A seh (d- s) r ('t)
Covv eYlte. a I fevV1 õJ J a V\o osc, [.Cl doy L C
Se. esc.olhev VvlLÜS plf=o:
~ EV1+~ : ~ -=: o9 (f,o) õ qo (""êl.() ("/,) A ~ 0
0
('3)
Ã.,(-bo)== o -/
5ubt;t. (9) n,*s soluções (0)' e.C=r) :
[9~~o Cos wtl (b.2) [r-~-~--,-0-.c-'Se-V)-wi--'---í(+2)
:= Á-o ((byvtV\te de ~) cQ)
Obs. Leh1,b'ról VI do gu e. -se" LJ: -= lbs (wt+ 11'~ I v~Vv)os que. él C~r~
3Gl esta ,;;dY3Sél dCl rol" Si) em vel a ÇólQ a eol'vevífe.
Eh eV8' õlS Cllrma ze Vléj dq 'S ( e/{f ..",Ca e V'vlõi3 he"-t,CélJ:
2 .' :<
Ue: ~ -i (10) U(3 ~ Lç (11)
( e. t;l p a C, \-to V' ) ( \ 'Y\ du to r )
e(b) 1-1- (1'1.12.12)
5U 6'3+. ((,.:2) eVV1 (10) e. (=t. '2) t-lrv] (11) I O bi emOS:
. 2 '2 { 2 2 2 (hJ '2 2-t
UE -:: ~ (}os wi (10.2) U(3 -::..i L W qo St:n wt:= ~ 5eVl W
2~ 2 zC
(11.1)
E~e~31~ ~o+~1 UT
ri
UT ~ lJE+ UE) -= * (Cos'< w-+ + Se.; wt ) -t> U. -= -i (12)
2C -- --v--- / '2 C.
~1
-oe.. (1'2) I ve vn os 9ue a eVlÔ'3'.;J +1a I ,s~.~:0..5-é'V\ld.
I d 2C Ur.[,,:29-(,: OSCI õI OV LC us+
t~'2,of F / t"v CJ:J ~ 20 v I L" 10,oF i-! o '1'11. 'f
a) :f ~ ? \t l. r (9 ' 2H 70 r")'7 lI'? : êl
b) ia ~ ? ~-re 'Sf e 2 (~a 11.): C, V'Cu do L C
2. C v (uífo RLC sem GevêJJol"
O gue élCo.;Jece se. eo!oc@yvYlOS Um reslstDV
I ?em se y, e COVV\ L e L hO Q/vcurto LC p
re( C1 (el das Vvl "d./hõl$ :
-I L ~ + 'R ~ +t~O I (13)
í\ ~)
'Vu CoWlO Á- -; 9 (t) :
L 9"(+) + Rg'<-tl + ~ co O (13.2)
A4. (13.2) el i d~v;fl Cél ~ do oscllador- mõissa-vYlOb @wv:::wte-
G,do:
W1 X\t) + b x '(t) + KX "O I (14J
As -e:9u,v-a1 ên ~\q5 (4) se. Clpl1cam hO'liC1YY\ô,,+e)
o\~Vvi de;
(15) ~"'''''+de. qW\ov1e CI Vvte~
Ou v-e 51s-+,va
A. solu~o dCl ffj. (132) t!:
19-= 9° i RY2L C,os (w\-f - 'b) L (10J
,-
0651: O StV1t de evolu1~o do -t;.SOY ~ ° élV\-LhOY,{V,O
j
Com veloc élhju!av W CoVls+aV1te,
01:0 :2 : A Com ~o neVlte X do fCJ $OY V-e~Jrcse;;f@.) é'h/]
C -a J a IVl 5 taV1 fe do -te Vv1~ (o vqlo v Ci+lJ~ I (I ViS+CJVi _
+â V\ t:o) d@ VYl E:-sW\ a : /W
R
~ L1v
RO
WS (w-f- s)
Tesfe 4 (HaIlJ -fa'SOves
3. "T~50VE-S :
{~I
s~o veioves b, di lIVIé'nSi Onql5 que
V'er Ir c SeV1 f Cl VVl 5 v 01V1de z.:S Cl/tev Yl<JdóiS
(c.omo ..t e LJ.V) ~~ue evoluem CDVlfov-
ir\n e UVVl a -19 se CVf.sc-eVlie.
2 3
J ) Üy dc,., a y A, B J C (tJ .~~'" (w+-~) Cio n10rm e <p .
b) Tõ)5Dves (b) >( CuvVólS (õI) ?
( . .-L . ?
C) Ç>UCi{ LUYV~ e d + éld'õJv1ladôl '
'\j (0
J ;:~ I S :o~ I 'd :c.0 I 'V ~ Y (9
'ti cP < <i1cp 4.. Jcp (E '.~