soex2-3723-06f - Problem 1: Derive the transfer function...

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Unformatted text preview: Problem 1: Derive the transfer function V(%(S) for the given RC ladder circuit given below where e is the input source and Vis the output response (note R, at R2 at i R” and C1: C2 ¢-—- :2 CH)” l 111%. 47/: 177%.. *2 v(:— as: :i/Ly—Lm ) I $32!? [ raids“ ) l at) [‘Crleif .7. V141!“ {2}} Vl':(7i_ C P- V ,0 g; : V2 i ) R1 ’0‘» (qr ’ ’5 V1 2 1C, 1K2) VI )H-l—f 3) firm 1004.21): 034/1: 3 ’9UU~C|€ 5):019YL:——1—— (33 34% > 73— % v3 3 33 I71 1'02K35 m VII 77/)", W11 Vfifl- : U (at R 5)=Ev:?,=fl':._l__n- 2 T‘CM’E") «4 its“) 4' “4 ’Vn—i kW ‘VZVH W W. EU) 45) 11-10) DEW 17,0} EU) *— ’ .ei__._J___, Vang/'5 t—Cg'tw (’cym l-CJfij Problem 2: Obtain an analogous electrical circuits (using force—current analogy) for the mechanical system shown below. WWW HWW-fié , Pro/alum wa/mt/q /Yll>f<'l Tblki "l" QLX\KXL);O W¢§G flap}; "(elm 7(2):. 0 "Vs-Wat“ ’92“; ’UAVI’Wfi/mlojv’ we Amt/a H ' “L” "L L "’ : Gflflzw 1m + L2 96. 92> a cl%+ Jig/(#2 “Pi—acc’éf’L‘zfio Ndl’a wast" yze/ N3 MVZ. ' re alt: fJ/Ze‘Jc—Jggzidti-i—zg (<7, z) o Page 3 Problem 3: X0 (5) 19(5) response xu(t) when the input 13(1) is a pulse signal given by Derive the transfer function of the mechanical system shown below. Then obtain he X,, 0 < r < I] x, (I) = . Assume that xn(0—) = 0. 0, elsewhere . 950%ij «lac/WW4 m y/slzm: k: (IQ—)9) 3% (990”3') 1 EM ed): ha 195?. >26 +1?! X6 g:le +1’Qy' by + ('23 =£2xlt Ndh/ (MAT X(o~)£0/ 2 (0-7,:0 (fa/43, 475m? WW (lawman): Wig/143+ we”) wig EMT“): 92 521(5) Etymwwhg TO); Luz/Aqu deg—eat mam: leg,- 0) T425 ==> EU) _ kud925+éfl EU) Cwmw-Hla, [42, L2 320W 1725* k2, Page 4 Problem 4: Consider the electrical circuits shown below. Assume that the input is sinusoidal, e, (t) = E, 005 wt, what is the steady state current i0) "? Please derive the formula fopr steady state response when the system is subject to an input of E, cos (at. grmvr Stui’e l/Mfl-Wfib _ jut xljkjfi +o~2 WINE paws, Eli—5a (St 2/97“ = H97“) 573??” E A¥9HLS)S{:;; Waving”) 1 awn») Page 5 Problem 5: Consider the mechanical vibratory system shown below. Assume that displacement x is measured from the equilibrium position in the absence of the sinusoidal excitation force. The initial conditions are x(0) = Oand M0) = 0, and the input force p(t) = PSiI’ltO! is given at t = 0. The numerical values are given as m = 2 kg, [3 = 24 N-s/rn, k = 200 N/mi P = 5 N and e) = 6 rad/s. Obtain the complete solution xU) . input force p(.‘) = Psin cor adafi'pm (1+ WWI—tine Tkxa/oajp’Pm/itfi‘ CXC°)~’0/ >60)ij iavtm Wmva =9 (WW/rt) Zw—“Pw Wm’zr L374, [$200, 17:5, was 5 fé‘e PZES); fi—LS;*_Z_ ...
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This note was uploaded on 12/26/2010 for the course ECEN 3723 taught by Professor Staff during the Fall '08 term at Oklahoma State.

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soex2-3723-06f - Problem 1: Derive the transfer function...

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