141_1_Chapter3_problems

141_1_Chapter3_problems - ftn-nflnw.vmmw(C F(s 3=t 2 152...

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Unformatted text preview: ftn-nflnw;;....vmmw (C) F(s) ; 3=t+2 152 Chapter 3 Dynamic Response 12. Under what conditions mi gnt it be important to know how to estimate a transfer function from experimental data? m (d) F{.t) 2 Mini"; Cs+2)(s2 +53+1Tj (a) 121(5) m Z—EM 3 +4 eanatens ace Transforms ate potes have coefficients that whenever comp lex (a) an) 2 ‘414 ’3‘ S i .' Review of Lapl oniplex conjeg ates. (The result of this relationship is that resent, oniy one of the coefficients nee g time functions: Problems for Section 3. 3.1 Show that, in a partial —ftaction expansion, c are also complex conjng conjugate pairs of poies are p 3-93 LIanS {13 fun p §C§m D h 0 g {Ianfi [[115 f the foliowin 3.2 Find the Lapl (a) fit) 5 1 + 2t (1)) f0) 5 3 + 7: + t2 + 6n} 3f (3) PU) : SUj—«QJZ (b) F(s) x 21W 3- m (c) fro n e‘*‘ + 2e"?! + re“ (C) F{s) : M (6) fit) 2r- {t + DZ (8) f0) 2: sinht StH-ifl (d) 1%} m flew 34716 (e) Fey} 2 zniw (-\‘+l)(3’~+4)2 (a) fit} 2 3 cos 6: (to) fit) :- sin 2! + 2 cos 2: + e" sin 21‘ (9) f0) 3 I?" "t- 2’2‘ sin 3: (e 1%) m (352:1)? (s H) (g) Fe) : tan‘1(l} S the following time functions: 3.9 S 1 , . 0 W the {0%ng ODES “5mg Laplace tfansforms' (a) fit) ~£~ ye) + 3w) 2 0; «0} m 1 '(o) — (b) an M 2m '~s~ no) 2 one) : iy “(om—2 (c) an + in) 2 sin aye) e 1. n0) 5—)2 ) m 2 (a) in) + aye) : sint;y(0) = E are: 2 (e) no + 2&0) u e’n/(O) 2 1 no} —; at no we) : cytO) 2 1, in» =:': Find the Laplace ttansfortn of (a) ftt} z zsinr 00} fit) x Icoth (c) f0) fl t8": +2tcost (d) ftt} fl rsin3r ~ 2tcost (e) ftt) 2: in) + 2t cos 2: 3.4 3.5 Find the Laplace transform of the following time functions ("F denotes convolntion): (a) fo} r: sinzsin 3: (b) fit) : sin2 I + Bees2 3 (Cl ft?) =1 (Sin 0/1 (d) f0) :: sin: a: sin: (e) no z fgcesn M I 3.10 Usin - g the con ' ' ~ rasponse H . volation integral, find the step res 0115 15 glven neiow and shown in Fig. 3-47. ‘1? ‘3 0f the System Whose impulse figure 3.47 Wake reSDORSe for {Gillan} 3.10 )sinrdr ansforin of f0) is F (5), find the Laplace transform of tit 3.6 Given that the Laplace tr following: (a) gtr) :: fit) cost on go) a If, 3‘.t'<r)drdn 3.7 Find the time function corresponding to each of the following Laplace transforms partial-fraction expansions: "i‘irne (sec) (3} 17(5) 5 5,1512) M 10 (b) FLY} ” S(s+1}(sm ...
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