Question

The vector-matrix form of the system model is: (18 0 18000 72001 x f(t) or Mx + Kx = f(t) 08.3. -7200 8000 | X, 3. (1) X= M = (18 0 08 K 18000 -7200 7200 8000 and f(t) = (1) 12(0)] [x₂(t) The system's eigenvalues, natural frequencies, and eigenvectors are: 1 2 = 400, 0, = 20 s', and v, 1.5 1.) = 1600, 0), = 40 s', and v, = -1.5 1 1 The inverse of modal matrix V = (1.5 -1.5 The mass-normalized modal matrix, its transpose, and its inverse are: v-LX *). v- ,J.und vº- 3 2] 3 -2

Answer 1

An SEVCHI Givm MX+KX: ris 18000 - 2010 :18) co 7200 8000 To find naturene frequencies: IKE.COM/ 7200 15000 -1861 7200 8000 - 8000! 8x19 (1000-60')': (7200) 12(1000-2002): 7200 12 (1000 - U') = -7200 12 (1000-60,), 7900 (9,1: 400 W: 90 rad/sec w,' 1600 W, :40 rad/sec Modal vector: ist mode: [K-um? =0 10800 -7200 X , 9200 4800 X Let x = 1 -7200+ 4800 X3 = 0 X: 1.5. V 1.5

and mode: rk 00M7 [%] 7 a10800 X, - 7200 -4800 X2 -7200 let X, al -7200 -4800 Xy = 0 X, :-1.5 Vo C-is] -1.5 Viivi Vo] Modal vecton 1 -- 1. 5 -1.5 1.5 vim vir -1.5 -1.5 JL:] 's - 5) la 13] 1.5 [ -1.5 36 VYMV: la - Mi = 36 36 To get normalized vector Vo: 1.5 an col- 6 G 14 - /

B, y,'m dro) 19 40 tm Vs 18 120 40 [ 113 [ 11 Ire 2 40 -] [6] ( ] [3] 36 0 40 3, 2 9 system responre: from U: Vni B, sinu,t + Yn, B, Cin wat IS VA 응 sin 207 +9 [4] sin not 3stn20t+ sin4ot singo7- 9. SINAUA 초프