Question

Question 1-4 is about the following mechanical system: Data: ki-20 [N/m] b-2 [Ns/m] k2# 10 [N/m] m2 At) mi Question 1 X1(s) Develop the symbolic transfer function G1(s)2 F(s) 1.1 Determine the differential equation, that this transfer function describe 1.2 Question 2 Sketch the step response for G1(s), using Matlab and explain the process 2.1 Sketch the pole /zero diagram for the transfer function G1(s) and reflect on the relation between the step response and the pole /zero diagram 2.2 Determine the differential equation for x(t) 2.3 Question 3 Sketch frequency response (Bode Plot) for G1(s), using Matlab and explain the process. Use a linear plot of the Gairn 3.1 Sketch the pole /zero diagram for the transfer function G1(s) and reflect on the relation between the Bode plot and the pole /zero diagram 3.2 Sketch the time response xi(t) for f(t) A sin( t) for some frequencies and reflect on the relation to the Bode plot and the pole /zero plot. 3.3 Question4 Develop a Simulink model for the response xi(t) for various inputs, and give some examples, where f(t) is a unit step and where f(t)s A * sin(w , t) 4.1

Answer 1

question 3 Solution:- Givem :- masses 1k14 1k2 Sprinand haing tension CaTC tro0 resp aiven dlata - 13 2 1Kg K2-10Nlm b2-4 NS/m reseele 1<1 eeeere above given diagram Por the drawn such thet Por Prec are free bood diagram of m, where PCt)= matemal Porce Porce (49 R ot) -damping Pore

aiven are where Bz d (arn) F(m)Me d) Pin)- kn where Be is damper Consta sprins is Constan diven by equilibrum equation The Mad(n) Rs Ct) + le, atp BapPlaing Laplace Arans Por mation ael bo th 5fddes of on the equation we L[RCH) Mdcai) +L 4 L d (x,-) + KL[M + BzL M2L tkixe) Me s2x ls) t B2 Sxi)-nc Ft () + bady Liagram Por m similars the Tree 2 12 F(n2) d2 2- F(b) B.dl (n-n, Ror m Theretore equilibium equatio is given M2 d (n2) Bol (-ni) +것2k2 In the case of m no extormal Porce is apdie d toit such that RoYce s equal to o'.

i.e, oma d2(a, - Bd (a2-x,) dt2 aPplyin Laplace transformations on both sfde we get 1e dCx2) ( i 1- - -BL +l dt OM2S2 X (s) Bs 2s)-,Cs) tka x26) Bs 22 (s) X2 (s) = Bs-Mes2-K2 substituting the value of (s) o St equation i.e Br) PI(S) misx, Cs) t Bs 2s) + 1x,Cs Bs-Mas-k2 M2S2X()+ Be s f2 (s) M,32-K2 s)+ k11,Cs Bs-M2s2- Punetion TransPers ( RA usB 1.e Gs Cs) ; Cs) Pz(S Bs-Mes2-k2 Mis (Bs-m2s-k2)- B3S (ma2 +k2)+Ki CBS-s2 k) Por 4)=A* sin (w-t) Given me respons e Ror (t) some frequencies Tor cheg have cer taln time init, I? you uamt Yule: In oder to 30ve this equation equation, we the ques ton seperaly Post Por answer Thanlk ou

Answer:- question from diven table the FBD CFEE Bodj Diagram of mass m2 Pb Here. Fm2= m2 dx2 dt Pbi Fk2= k2.x2 From the newton's law of motion Alzebric Porces SUm of cll Sum ot reactive Porces gum f Applied Rorces f Pr +Pbit?k2 TYP t k22 t t b of mi mass F.BD Phi (4) Fre Fm, =m, dx Here b

From the newton s law of motion Sum of all Porces Ngebn'c sum of al eactve Porces P=Pm,t Pb+PK ( P(t) =m, d2 dt bi arc the cifferent equantion s Yespeatvely equation &6 CA

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Pttin ie valur s) +B,s x, (s)- 2 Sx2 Cs) 2.S-M2st +K,x,C) BS-MStk &s-M,s2- Ke Bs-Mis-K Gs Cs) X2Cs MS(s-m,st) - 2,s(n,sk)t,as-ms) Tronelia Jundtan ysh