% 无阻尼二自由系统固有频率的程序 20180401A: s; s+ ]* S1 T5 z4 H" n# w9 ^
m1=100;m2=100;k1=200;k2=400;%
$ r; ?' k4 [* W0 N3 A. z2 C9 I5 \c1=0;c2=0;: Q. k2 w, T# E: P* h' w8 U
x0=[1;0];xd0=[0;0];tf=50;dt=0.1;
. z9 `: Y" c+ D0 u0 eM=[m1,0;0,m2];k=[k1+k2,-k2;-k2,k2];
b' E) V- m1 Z3 Bc=[c1+c2,-c2;-c2,c2];
; R- M- e; l4 z3 y6 \A=[zeros(2,2),eye(2);-M\k,-M\c];3 A2 ]# m. {, a0 G
y0=[x0;xd0];" n# {3 A R+ l% ^6 N7 S, T
for i=1:round(tf/dt)+1
1 v3 z9 \% n9 m t(i)=dt*(i-1)" `/ E6 B; o$ i. c
y(:,i)=expm(A*t(i))*y0;
( ~) s9 C. @( send
* U L* V8 Y; }: m$ `+ Wsubplot(2,1,1),plot(t,y(1,),grid 4 ?+ Q2 Q7 O- Y0 p, e* z
subplot(2,1,2),plot(t,y(2,),grid/ p* l3 h `# p7 A6 ]! A* O# Z
[p,lamda]=eig(A)
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lamda =" s( m( q6 Q( L4 j
Columns 1 through 2' x7 ?: H" v( W. H
0.000000000000000 + 3.020447918044219i 0.000000000000000 + 0.000000000000000i
" l) S' g; I5 @ L/ ]; i8 U 0.000000000000000 + 0.000000000000000i 0.000000000000000 - 3.020447918044219i
: J/ S. ^+ E! W, [2 ]. [ 0.000000000000000 + 0.000000000000000i 0.000000000000000 + 0.000000000000000i* N# A! M8 L2 z( ]
0.000000000000000 + 0.000000000000000i 0.000000000000000 + 0.000000000000000i1 M) R& y; p3 b7 ~
Columns 3 through 4
# _& X: }3 `+ w C/ S 0.000000000000000 + 0.000000000000000i 0.000000000000000 + 0.000000000000000i
& F: H; H$ g: o2 L. G 0.000000000000000 + 0.000000000000000i 0.000000000000000 + 0.000000000000000i
- {2 |) l0 k* U" I( x0 b -0.000000000000000 + 0.936426384924271i 0.000000000000000 + 0.000000000000000i. E' d0 H) _+ x! {7 S. i' y
0.000000000000000 + 0.000000000000000i -0.000000000000000 - 0.936426384924271i
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