Sotubi.'. SzRuc {- bl+r. !:'z: (Fall 2016) ELEC 341 Quiz #l. ?), Ztz- SA{: Name: Uv.

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1 nstructions:. You have 45 minuirs lo complete this quiz. o You MAY use a formula sheet and calculator o You MUST show your work in your bookl t.. You MUST write your answer on this paper (Fall 2016) #l Name: SA{: Sotubi.'. 1 - (5 marks) Use circuit analysis techniques to compute the trarsfer function. l. l^ TT _,, u - vl R C L + Y :,2 2-(l 0 m a r k s)!:'z: Uv. SL SzRuc {- bl+r Convert the circuit into an equivalent Signal Flow Graph markg Use Mason's Gain Formula the Signal Flow Graph to verifu your answer in euestion #1. {Don"- see work in booklet 4 - (10 marks) Redraw the Signal Flow Graph as a Block Diagram. Label ir and ir.?), Ztz- \J' 5 - (10 marks) Use Block Diagram Manipulation to veriff your answers in Questions #1 and #3. Q/Done - see work in booklet

2 nstructions: o You have 45 minutes to complete this quiz.. You MAY use a formula sheet and calculator.. You MUSTsho\a your work in your booklet.. You MUST wnte your answer on this paper. (Fall 2016) #2 Name: S/NT. Solut i""t frl tglnecrlng 1 - (5 marks) For the following SSO (V is input, v is output) mechanical system, draw the equivalent electrical circuit. Label it using electrical symbols s/, v, R, L, C).,v -_> V - K : N 2 - (4 marks) Compute the transfer function T=v/V of the ELECTRCAL system and represent it in NORMALZED form. rg): ffi: W t/r. 3 - (2 marks) Compute the transfer function T=v/V of the MECHANCAL system (V, v, B, K, M) and redresent it in NORMALZED form.,g)=ffi= bz* Y^q sb/,t+t7m 4 - (5 marks) Compute the following values from the MECHANCAL system transfer function. Reduce the terms as much as possible. Compute final value for the NATURAL response. a?jea U - a J -.\ ^/t 6t-\ Koc = FV= t O 5 - (9 marks) Plot the poles and zeros assuming that the system is as labeled on each set ofaxes. Label all real and imaginary values and indicate both o and on on each pole/zero plot. LJ^ t J --,^Jrt JYn +J Y^ z 1 u.jl Critically Damped

3 nstructions :. You have 45 minutes to complete lhis quiz. Namg:. You MAY use a folm. a sheet and calculator. You MUST show your work in your bookjet. e/nt. a You VUST wrile )ou answer on lhis paper. (Fall2016) #3 *j glnc0fns A deranged ghoul wishes to discretely transport an evil pumpkin, for sinister reasons that are best left un-said. He uses a delapitated baby carriage to conceal his wicked cargo. The basket of the baby carriage is supported on a suspension comprised ofa squeeky spring. After placing the evil pumpkin into the baby carriage, the suspension compresses by 4 cm. Provide all answers to 2 significant figures. Mass x2.5(kg) g =9.8(m/s2) Mass x 500(9) Mass x 125(Kg) V Al = 4.9(cm),f Spring riction * 7.8(Ns /m) 6 - (10 marks) Draw the equivalent mechanical system model ofthe baby carriage carrying the evil pumpkin. Compute the values ofall associated masses, springs, dampers and applied forces. F= l'j, faj Mt\ - 3Kl K: fcs> tj/rn R: -7.8 N':,l.

4 7 - (10 marks) Compute the normalized transfer function. r(r): F6: t t - t3t Sc:o $z*2,6g + 13' 8 - (10 marks) After the evil pumpkin is placed in the baby carriage, how long does it take before the baby carriage stops bouncing around? At what frequency does it bowrce? rime: 3,1 E Freq: 13 S 9 - (10 marks) The baby carriage is old and wom out and the suspension bottoms out if a 4.5 Kg mass is placed inside it. Does it ever bottom-out, even just for a moment, after the evil pumpkin is olaced inside it? Prove it. Bottom out?,", 1n) " \-_/ See booklet forproof 10 - (10 marks) How much is the motion affected by changes to the size of the evil pumpkin placed inside it? s it affected more at high frequencies or at low frequencies? sensitivity is higher high freq See booklet for proof

5 nstructions:. You have 45 minut s to camplete this quiz. Name :. You MAY use a formula sheet and calculator. You Mf ST show your work in your bookler. C/f\T.. You Mt ST write your answer on this papen (Fall 2016) #4 t$r [!lrccrlm 1 - (3 marks) For the following system, compute and plot the closedjoop poles & zeros when K:0. s2 +2s+2 "'*4"*8 2 - (1 marks) dentifr the parts of the rea.l axis for which the root locus exists. Realparts: S ( Cl 3 - (1 marks) Compute the assymptole angles and assymptote centre. A = lqrho (r'' '\!r- \ \)(:= ) 4 - (2 marks) The root locus has two breakpoints at (s = - 1.2, -3.2). Are there any others? f so how many? Do not compute the breakpoints. Just show how you figured out how many there should be. *. J+q*- er(**?r*z)-r 8.*zX*+'{**8s) :@ \ s t- GH 3*+ gs+8 str2s* L (s"+zs*z)z ( st*2: *a{:f*8s"8)- (2s.")(51+{** f,s) = (D H*l oj", Total number ofbp : 5 - (2 marks) Compute the departure angles and sketch them on your worksheet. DeparnreAngles= f \q gt 6 - (2 marks) Compute the anival angles and sketch tlem on your worksheet. t. AnivalAngles= + lo8' 7 - (1 marks) Compute the raage ofk for stability. Hint: complete part 8 before ansering this just in case you notice a very easy way to find the answer. K(stable)=,K 8 - (3 marks) Sketch the root locus. 6y.nspe-c-fio". of R-L

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