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Solution Manual For Theory Of Vibrations With Applications, 5th Edition

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    Solutions Manual-Theory of Vibration with Applications by William T. Thomson and Marie Dillon Dahleh TABLE OF CONTENTS CHAPTER 1 1 CHAPTER 2 9 CHAPTER 3 41 CHAPTER 4 76 CHAPTER 5 116 CHAPTER 6 149 CHAPTER 7 178 CHAPTER 8 201 CHAPTER 9 229 CHAPTER 10 249 CHAPTER 11 350 CHAPTER 12 366 CHAPTER 13 412 CHAPTER 14 438

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    Downloaded from StudyXY.com ® + StudyXY Sd Ye. o> \ | iF ’ pr E \ 3 S Stu dy Anything This ContentHas been Posted On StudyXY.com as supplementary learning material. StudyXY does not endrose any university, college or publisher. Allmaterials posted are under the liability of the contributors. wv 8) www.studyxy.com

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    yi 2 = A su Ot A= 0.20 ce Y=o0.i5s Da ZW _ a/.89 Ms 7 L = WA cos wit x = WA = 8.35 Omi . Pred es nda x == A sow JE X may = DA = 350.7 om/s2 -_ Tm Tr = : - Wa 2Tf =27xgz2=5152"% WW = 0.2655 x 10 2 = 980.9 <m/s2 x, = % Wr = 50x 980.4 _ , seq wr = Fr Gacssx 106 TOE om - oo / —-3 D=2Tf = 2x0 = 62.83 2; Y= £ = 0.10 s Fay = DA = 4.57 mp A= 0.07274 m = 7.274 cm Koay = SA = 287.7 mss - d= 4 % = Asta, t tsaat) = 24 ca f(a) “Sot (ag rel, ) let w,= 0, Wom WAL, Qa, =2D044DF 20 sox FT 2A cost AE - sant -_ / —5 is 5 i Z=4+3. = 5(wmo+isdug)=5e re’ <) 6= tas = 3°52" = 0.¢435 & 4 -- L=6 =-6 ‘oe : z=4Ae A =7¢*+ 2% 2 6.325 2+3¢ 4 = ¢ _ -7 °o Sum = ¢ +2C 0 Tw2 = 7/872 = 032/17 : z =c.325 ¢ OT 12 ew = 6.325 [/8°2¢’ A ! + StudyXxy

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    , z= A (cme + < snp)=Ae’ z “ . . . / cz=A(iCme ~Same) = Z, ° z 0 A =Alea(o+ 90) + Csi (6+90)] ® 1-8 Z=30° R . A * R =5+4cos30"=5+3.47 ’ 4 CP = 8.47 4 ; R = 45m 30° = 2.00 Var At R=) 847% 2.54 = 8.70 6 = tan” 2 = 12°57 £=9 id X(t) is odd Function i GuzO % t b, = # [rarcmmat 4 “% = 5 < = 27 bor = Z 0 4, = | fensmmnt (— | 4 “ o Pe Cw mnt | _ emawt |B] a = =x on =F (1mm) iz o bh =f0 for m even ” = » m odd Kly< 2 (simu +f Smit + Fomsits os) 2 + StudyXxy

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    L=i0 . . x(t) Z(E) is even function bu = 0 | il "owt Ks ou fmt | “% ar d r= pus Wz mw, -% +% ’ Tr a, = # Jeans dwt) «4 fer emme dtoy “4 Jem nt de = SA 7% rd —fr m= 3 7 4, --- 2) = 2% (cout -Fcasut +L emsut-o-) I= 1] ro a(t) & even function bozo L(t rm -Tx1s0 = > wi xe) =[# +7) wr Z(w-1) o<t sm fa, = average value = # ° Tr G, = £4 (t+m)casnutdiwt) + £3 (r-t)cos mast d(wt) - 0 kid = z [+ (r-t)cos maw, dlw,t) because of symmetry ° ats wt _ 2 sa + _ 2 (emmat wt sum mat =F = | 2, (moet rs <) o ° = [0 Hr nn even Ze for nn oda NCCT It £ wast NY, 3 + StudyXy

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    I —i2 Lo x = = o0=< wits 2T Zz ot a imwt 27 c = wt oo g 97 = 3 ar © A [4 = vd c na He —enwlt p ime . » where on = wt € Wt) = L — [-en6-— rf ’ 49) or | Ee (- J o-ut o [2] = [- + (1+ ¢amm eo z 2 Tent mt J ]- rom ’ : (ut owt Lawt iz sat isu Pi ; ) ) 1 Gd ] COBRA 41 -e )+i(e ~e Get (e e Tr] . - Lg, a. 24 2 [shaf +f Smant vf Smut ] 7-1/3 wt Oo z Fat Ll Io = reo 2 le A x fd [4 set dt = Lm 4 [sm corer) ar o . 7 0 lm A(t Sm2at)|E A sel : Taw -3¢- PTX) ) sd (% or )= 4 2 eR CE EY re) £ wt) 2 Ll 6% ox gsan _ or 5 AT [A x* = L rot = L [L (4.5) =z) J o = t Loam — =L (amy. 4 = a ( 5) 3 4 + StudyXxy

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    L=/4 cont FS. of saw tooth wave = 2) = 4 — F(semet + smart rd soswte--) whe) = L yore Ce . =) (¢) = 7 —F (smawt +f saw, ro: . J su 2 +45 (sw wt + 2 Sew ze tens) = —E (some Ea TA --2) ~ 2 - 2 .. cross products which c(t silt eee) + 0 infgeute to zero £ oo pr a T B 1 cosdwt r x(t = L Cosaw,t L_ coawt Cos 3a +f ) 2 * rar ’ AT ‘ *qmuT ‘ | ° ° o 0 Lo L(y sezwt)|T 1 L sgt (T rir tl wo) ap EE Fable o 0 Let WT =2T£& where #15 an Steer —> © rk VLR AC = a 1 L 4 Lr * Te a | <oas = dtm tian TE Gm o = -- A SERA CRF EE ) = 3 1 =15 —— Xt)=+% + =A (coset +4 cnt + LCST +-- 2) Fourier Spectrum = plot of Coefficients. For His case b =o Co=Yaitb: = am Ces § 5 405 -135 .08 -5 -4 -3 -2 -/ o 7 2 3 4+ 5 mm > + StudyXy

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    [=e 2 “ #3 [2%4 a c= 2 = average value= AT £ =f a, =L senmbr = ol su mar = - = L (I- ex mam, b, =L ( csmbm) = L (1-cs pT) - T_T [rrr ad 2 Com Yar + 5. c= (7-22) 2 === mm [= Be mm Ca [2 / . 275% -é60° <4 c0689 —¢o0® z 1375 60° 5 0552 co 3 ° ° JA ° 0 Cu EN é. A: a ~ IN °o / z 3 4+ Ss ¢ ~ 2 3N aA 4=i7 Len —S = hemo + Leng £ Ling = nsand 5 — = 2) ” ind =[1-Gfs'e] ) - um 2 nE ton = 1-43 fords - 4 (35% Ss nli-emorg(f)sido f(s vo] using Sms = L(/-emz0) 3 some = £4 -20026 + {ens6) S=t[i-cne rE) cm20) 4 --- } ) = - —L/n _ which retains only =rnli+4(%) se £(3)en2e +---] ® to First power Ratio of 2h armonic S15 far monic =4(3) = 7% 6 + StudyXxy

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    [=/8 T . KE = lim A A . A RY | gat * Too +f (dt > A . ° = 0./10A noms =) xz = 0.3/62 A - L=19 x = (1- Z) ost = 2. 2¢ 2 *= = s L, t= L i 2t * £ 20-2 Ea - 3 TE 1 —20 % - Db =20ly (F) = 0.50 % |. 0-50 _ lga(%)=%22 = 0.0250 * = 70 9°%° _ 0593 (3) Se = 4 %,=10593 % = 10593 x 2.5 mm = 2.6458/ Error = 0,0593X%X 2.5 py = 0.148 mm ma De sm bye) 20 Db = 20 log, (50) = 33.98 Db = 20 log, (100) = 40.0 ~~ x = Zp = Db = 20 go (3) = 32. ~ x ad = 32 L.(2,) = zo =/-¢0o % leo = = 1/0 = 39.8 1000

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    | —- 23 PA | — = J = (-1)= 0 [— I oR ar Ta 8 a 1) Pe — - 25 oo J (2 FA C= JD = 00 (eld Fuckin) EYL (ICDL FO) = ED ever archon)

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    2=l— EF 229 ro. 576 5.7 - 5.42 Hs Y 4 wm V7.57 = 2-2 ~ YE N fi NEA %- (kk) £ t LY% = [ZB [X 2 J = Z%5 1 = Xk oo ky =F Ek 4 frih ix BERT re a 2-3 14 t 2.2¢kg «4.53 ky. 2% iA = 0.455 m, 2.24 2 7 % =m) 2 = 2m [Aa Ke (Lf (5) 05 <4 xg83. = 883.5 N/m = 0.159 s 9 + StudyXxy

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    2-4 2 _ x 24 \* * (am 77)* 2. (mf) = (2m 2) peor =(2 %7) mor 453 * , _ as = (2) am = 0.9028 Ag £ = 87.48 M/m 2Z=5 % measurca from static eguibibriam pasitiin of m, A k £q. of mation after impact "2 23 ny (reo) x = —Rx + ™, 3 IE + fx Gen Solution’ V pA 2(t)= ad 4 Asoo + Bomal x mg Ld condita: x2(0) = © = xd +B iB=-T x(o) = Tergh = wA vA = ™af2gk my 7m (mt me) GE —_ w= ] ~ ry cox) = Tad ow mylgh Yon pu z TBE Smt — 3 em wt = Tt (1- emwt) + mah ot e Yh(mro,) PE % = x, HWE + Sue WE = 2enzt — Sem 2¢ i = —45m2t —femat =0 lam2ia-2 So2t = 116.57° San 16.57.8944 nie. 5] = — 4472 Kppay = 2(-. 4472) — 4 (.7944) = —4.472 Cm Fora = SH, = 4(x4.472) = £17.59 em/s* 10 + StudyXY

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    . . . 2-7 7,6 =-wne 5 = -we J. Wa o Tox o 15.83 A > T T2 rr GD) ) © Y SJ -HA = _70,¢" il J = Jp Fi = /5.83 ~ 300% Je = G.30 bon sec” I J 2-8 @ =m 82 = 555 nh = Wr 2/35 x.25% 5/76) ge A : 20.355 25%" m® = - 2 = 0.76) = FELLESE = 0.0356 % fy 2-9 Ro = Be Work dene = change in KE 2 2.2 +z zz | a= 2 w# Eh Ral ™ ! . | vertical displ = J= wu k= rad. of gyr. 20 ene =e[1=(1=F4)] 4 set ge) WaT. Wt” | 6 To z 2 I g = 2Y: = 2542 217 9.81 = .2032 « JE 27 1.829 = .4507 mm Shall A J 2-10 Moment about Shaft = (Stn) wr Simo [ET (T+ 58) § = - (ase) wr sin / ANG RES ? | ai YS NY z — (awsme) 6 ody / ‘ ro Ie / yes w Tur / Cm Taw Jr Yet / | j= pamlicl pfereicte planes / 7 + StudyXy

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    2-0 I" 2 LL 7 = Fm - £# J, 6 6 = x _ FA .z . f(m + =) x = wx _ . i 7 _£ U = $42 GQ =) mr Gipt - TTT Crm 2-1/2 2 _ LC - ZF 2)" Tear) L= 3(5)=s5(E)= 0.9% m C =L(w8) = 903/75 ms 6 = =I 7a s820° - A 231 ct a 17h = 5, TZz=/3 a YY — Z=/3 water weighs F80L.M/m> PRIA 98012 TR, Ms busyant force = MA xp 2 mE = Sx Lo. x =) ~~ m = 0371 Ry wr BE 2m Tre 2 = .0032 m ~~ 0372 = a = . ! es 97 5 2-4 moment bout geo. center .. x -wge = J & = -0 J, 6 . Jo= gw gw U3) ae ww ° w? (afm) Zs TT . Ky —-wWhke =J6 = -2DJ6 y. J 5=Z = YZ = am f= [ETS pd r wh Z-1g Dispt. of <5 “Bid Tay = Um 2.2 ad «RE T= fmr-R)6L + # iy Omen As a a * A =f m[(e-A) + (RAY [Wek i = ~ - =X Unie = mg 7 (1-c6,,) 5 mga Ea 12 + StudyXxy

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    2-16 cont Tay = Unies . Rg. _E_ WF ROR) Rr (RPE) 2R(R=F) IR(R-1) Fe AR . = YR(m-2) ak = but 7 = AE oo Team Z J 2-17 ~ 2 = Uz mgh(i-cng) 5 mghtd xp=ie 2 2 a2 _ £ [a6 |" = a” 6 sms E22) TEA ~ ERE ie Let T-g(mk)é" = $05)" . LyE Trang = Umer ERC a wre TE — ~ PE 4 ia FH For ly T-= 3 mp we L* e* . U="55%% Ar sam EE = LYE -h/L a #2 b= Sl [7 (£) em er 2-19 x wba 8 a wWab 6 b IM= JO == TET ww & wa wb ate a+b are wre s Wab gp =o b ta # “ ° § + (928 )e =0 t w x | i | wb as ( wt) , , lam ow N , Cop. L Y9eb ry > 10 .e ka amr Pal Plan View wa ra 4 . = 0 Zh 13 | T= StudyXY

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