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% 無(wú)阻尼二自由系統(tǒng)固有頻率的程序 20180401A- t# q; k/ T' t; k8 ~
m1=100;m2=100;k1=200;k2=400;%
9 A# |( k1 U6 ?$ u/ |c1=0;c2=0;
7 a7 c& s5 b# S. T+ zx0=[1;0];xd0=[0;0];tf=50;dt=0.1;
3 N x" l& S4 [M=[m1,0;0,m2];k=[k1+k2,-k2;-k2,k2];% c i U4 f( K( w
c=[c1+c2,-c2;-c2,c2];6 V/ T! s+ `% _2 w
A=[zeros(2,2),eye(2);-M\k,-M\c];
/ n) ^6 M5 F$ }$ e# p9 o5 Cy0=[x0;xd0];: D B N* w! z
for i=1:round(tf/dt)+1
* \" c; Y' J3 u t(i)=dt*(i-1)0 w& k& r' K( h z' @+ t
y(:,i)=expm(A*t(i))*y0;4 D; @% E. d& n, f. b+ ]
end
z/ Y6 j% p( @4 o* isubplot(2,1,1),plot(t,y(1, ),grid
$ K B, l& Z1 n% g& F! E8 i/ ^ a9 ]* Xsubplot(2,1,2),plot(t,y(2, ),grid$ r, P$ b" ^1 e0 _ Y
[p,lamda]=eig(A)* d1 H- \# ` ? K
8 @1 j1 A2 n6 Y( X7 t; x
3 D0 L# ^$ }0 F( f7 ~9 J" c Q2 R2 n6 F* W% v1 m8 e6 |
1 K; n+ d, O8 Y3 v o' _9 B
lamda =
* {( J/ V5 e: m Columns 1 through 23 J/ I# [7 S; t' A0 l% R
0.000000000000000 + 3.020447918044219i 0.000000000000000 + 0.000000000000000i
1 p* j0 ?0 T9 D: x0 T5 d 0.000000000000000 + 0.000000000000000i 0.000000000000000 - 3.020447918044219i8 M9 m* o' f7 F* w! P6 g
0.000000000000000 + 0.000000000000000i 0.000000000000000 + 0.000000000000000i# F R6 `/ o. s- Y0 l: u& R
0.000000000000000 + 0.000000000000000i 0.000000000000000 + 0.000000000000000i
+ \- D' _) n4 k# u# v2 v6 o Columns 3 through 49 t6 o4 y1 U; M8 \8 X+ s) o: P
0.000000000000000 + 0.000000000000000i 0.000000000000000 + 0.000000000000000i: e- E9 O e% o: m5 r
0.000000000000000 + 0.000000000000000i 0.000000000000000 + 0.000000000000000i
8 D; Q. _6 l, G9 Z6 v, D) T$ @ -0.000000000000000 + 0.936426384924271i 0.000000000000000 + 0.000000000000000i
* F2 A, a: W. J. }6 R1 ~+ } 0.000000000000000 + 0.000000000000000i -0.000000000000000 - 0.936426384924271i
4 T# [& B/ X" V, k5 F/ G9 n9 a( i1 u6 e) [! r& _' Y
3 q$ P9 R) t9 R! u5 t% E
% D2 F. w: L7 m# j0 ]
# ^0 P9 v* T( d9 X! K% v |
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