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% 无阻尼二自由系统固有频率的程序 20180401A& s3 z/ R( @# f" \ m1=100;m2=100;k1=200;k2=400;% 3 o+ K3 Y: A- X; E5 Lc1=0;c2=0; ' A" |1 Q! e8 D% b5 ex0=[1;0];xd0=[0;0];tf=50;dt=0.1; ( {5 z) s/ M6 b1 Q t( R0 S- O. nM=[m1,0;0,m2];k=[k1+k2,-k2;-k2,k2];1 n4 z" P) M, q c=[c1+c2,-c2;-c2,c2]; - A1 s$ @8 y: X+ X2 R5 a$ d; vA=[zeros(2,2),eye(2);-M\k,-M\c];* A; U6 P7 [- P7 v y0=[x0;xd0];/ c" r7 p3 S9 F, A. Q5 g$ _: M for i=1:round(tf/dt)+1 5 u* e5 _, T! O9 p* B6 }+ _- [t(i)=dt*(i-1) # J4 {$ V4 e \5 k) k) C Cy(:,i)=expm(A*t(i))*y0; - z0 [# |7 d* Pend ! Y5 ^9 b5 ~; n9 F6 ~subplot(2,1,1),plot(t,y(1,),grid; ^+ `8 j' p9 _ \ subplot(2,1,2),plot(t,y(2,),grid) ]% E5 w- u& c1 ]. B [p,lamda]=eig(A)3 f* Z0 N; R$ |: C' D
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# d6 [* Y5 E% f6 a- `% z. f0 E- V4 d0 y( { lamda = . h# n. Z. A5 N d2 f- JColumns 1 through 2 5 S( h5 j' V* g" i! S0.000000000000000 + 3.020447918044219i 0.000000000000000 + 0.000000000000000i * z4 h& Q4 L# C$ s1 I8 i0.000000000000000 + 0.000000000000000i 0.000000000000000 - 3.020447918044219i) J* D! V% t6 v 0.000000000000000 + 0.000000000000000i 0.000000000000000 + 0.000000000000000i $ {+ ^4 x9 I/ ~+ e8 b# V0.000000000000000 + 0.000000000000000i 0.000000000000000 + 0.000000000000000i9 S5 d }2 S o2 c) F" V' X }3 l Columns 3 through 4 ]; I) I9 O6 |7 x7 {0.000000000000000 + 0.000000000000000i 0.000000000000000 + 0.000000000000000i% r) k0 ^( m3 h 0.000000000000000 + 0.000000000000000i 0.000000000000000 + 0.000000000000000i1 T$ z0 a# r D: t -0.000000000000000 + 0.936426384924271i 0.000000000000000 + 0.000000000000000i. L( j7 k; u6 I: Y+ d 0.000000000000000 + 0.000000000000000i -0.000000000000000 - 0.936426384924271i5 j! |" T$ ^9 k
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