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soex1-3723-06f

# soex1-3723-06f - Problem 1 Describe the following signal...

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Unformatted text preview: Problem 1'. Describe the following signal, x(t) , in terms of some basis functions (e.g., step, impulse, ramp or sinusoidal): 74:76): BuafﬁBW/Eﬂf; rd~g>~rr.5u(x_g ' ““16 y (#4); fthﬁﬁ’Q) + 1,; YUP?) “(Kt/Loki? —|:5 €007; {t ~3) wit/3), ~t-5’s‘h—{2L champs) ﬂaw/3706+ 1,5rbw)~r1.rubw)‘r3m~2) l satay J-j’ tux/3) 15mg mam?) ~15<h1mr~§wwsj Page 2 Problem 2: Find the Laplace transfonn of [Re 4" sin(w/1 — 6)d}t 0 of (301:7? {man/mmm—mej wwsa ._ 39w) , LJCOSQ’SQ’HE} ’2.— 7/ ._ L l 3 “J 9. TA) ‘ 2% if [gm LLJQ’éﬂ [mfg __ # i wassertsﬂ smO __ (5+3;21+w7’]("§m9)- Mose/carbwc} f as “L b (J [%¥S)fldu (516)%fbf1 2 J C 2136') _ 3M9 WWI/«13\$; [9%) (WW—(Mmsﬂ SIHQl[SF3JWJjTAUT3)£wC059ﬁr 0: , .— 5 fC§f3)23cr/J"]2 2% Page3 Problem 3: Find the Inverse Laplace transfonns of ”In 4“")? 2 g +25 d5. Problem 4: ProBIem 21". Determine the Laplace transform of the following signal, x(t) , with ﬁve periods (only three periods are shown in the graph). xlrl , ‘ W17): V L05 35 7t fbtli'}‘u[7kr2.)’] : VWSZ; may V Crag (barter!) uewz) : Vtog’lg 11,100+ V or}? {7m} new) ~35 EWV 9ng +17 32%;); 1, *Uslm'u) 7/ CHE? Emma/[71%; 1 SUN?” Lg? \$5774? #615 Dr Problem 5: Solving the linear time- invariant ordinary differential equation d ytt)+ 4652—0 _ 0560) (2’12 dr +13 WU) _5 dz + 6x0), dy( ) with initial conditions and inputy(0)= 3 7 2 —2, x(t) = e‘q’uU) , where y(t) is the output 1:0 response and x(r) IS the input signal. Find ya) and lim yo) via ﬁnal value theorem. VHF? ﬁghter) > 27523 S‘l‘f‘ ﬂu'l‘é %(oﬁj:0 2 A an J Q3? T4 afﬁrlﬁwr ”+670” 416 r, t a. . [3 To)" S2&9—‘0 ‘°’]T4[5i7(5’?‘“£lﬂ3 7f”) > *’ "5i5'2rr/ -’)<”/J+6]er) tsﬁﬁrs—m'ﬁv: (*55'+é)Z{S)—rG5a2’)_Haﬁ ﬂ..- "' (“5%)5-izf H35 H6) ( §s+slcgrc35+rogcrw Sti “\$5M Y6) :: m " ﬂ —l if 445 +1 3 ) (Wt) 85451-1} 5+4 MC +§~\$3+4émaéﬁ kl: [Sill—5"” llsjﬁ E’Hbtﬂ l3 2 5+175fﬂ:( We ”(5:49le 5+‘F51‘f3/l (wig T (ﬂaws) 5r Wat“) Page 6 ...
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soex1-3723-06f - Problem 1 Describe the following signal...

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