% 无阻尼二自由系统固有频率的程序 20180401A2 p6 M( |0 k- v* a' ?8 T+ e
m1=100;m2=100;k1=200;k2=400;%
8 X m+ @, ?9 ]/ Cc1=0;c2=0;" x: b4 E& o: g7 R' l, q' ~' K- n
x0=[1;0];xd0=[0;0];tf=50;dt=0.1;
% W; P! S: S$ L9 Y8 wM=[m1,0;0,m2];k=[k1+k2,-k2;-k2,k2];2 Y8 t3 y) G9 S2 L# D0 G
c=[c1+c2,-c2;-c2,c2];
_ s8 U5 j0 F1 V/ Y8 o: Y) ]! SA=[zeros(2,2),eye(2);-M\k,-M\c];
- j. n, w8 O# ?" v/ Z0 my0=[x0;xd0];8 ~2 ?% P4 J1 d$ j/ p* @3 B
for i=1:round(tf/dt)+1
. D& o) k: A1 \0 x/ F# e t(i)=dt*(i-1)) i7 k0 N1 I8 J0 [9 a6 k( m B
y(:,i)=expm(A*t(i))*y0;
% p" w; ]2 q5 z+ g) y6 kend( ?5 D' O8 x& X: B3 U- O
subplot(2,1,1),plot(t,y(1,),grid
- h& n' X; ?6 r1 ysubplot(2,1,2),plot(t,y(2,),grid
& P& ?/ {+ ?2 V4 O[p,lamda]=eig(A)9 X# q3 K2 J# P9 F5 ?9 }7 t' {
$ o2 y$ B# o& W" N3 R: ?
B J g5 m8 F- U4 q7 {
9 h( f0 x: |1 A! _& F* ?
. x& D% ^& ~) |. y, R6 S: llamda =
2 B0 M8 w; F+ w; U( b; n- o0 e Columns 1 through 2 Y4 T8 `9 G) x! v
0.000000000000000 + 3.020447918044219i 0.000000000000000 + 0.000000000000000i
+ _. @& `" {+ C# L+ ?- y+ |2 j 0.000000000000000 + 0.000000000000000i 0.000000000000000 - 3.020447918044219i
) M( y& _% Z4 L 0.000000000000000 + 0.000000000000000i 0.000000000000000 + 0.000000000000000i* m" V( E7 ~7 J& ?* Q
0.000000000000000 + 0.000000000000000i 0.000000000000000 + 0.000000000000000i
% z2 v7 n! |3 E W/ E+ Y8 E1 [7 y Columns 3 through 47 |" F- f" u0 ~( J
0.000000000000000 + 0.000000000000000i 0.000000000000000 + 0.000000000000000i9 _$ i) V1 _3 V/ A3 V: E6 m, g' s( i
0.000000000000000 + 0.000000000000000i 0.000000000000000 + 0.000000000000000i3 S0 I' P" T& w/ r T" G
-0.000000000000000 + 0.936426384924271i 0.000000000000000 + 0.000000000000000i
9 O2 c- U S7 ? 0.000000000000000 + 0.000000000000000i -0.000000000000000 - 0.936426384924271i
" s& S4 A2 s! ~% W$ w# Z& {0 E% F3 ?/ a( }
8 @; G: Q& G, v' d' C% U
; j: L' X/ H$ r2 \$ g7 U" B
a' s& F7 l' g* q |