% 无阻尼二自由系统固有频率的程序 20180401A
. y2 }5 ^7 G \m1=100;m2=100;k1=200;k2=400;%
' \" D1 T) g( `5 F- Pc1=0;c2=0;! q0 Y! G5 d5 S, [- z* }! W z
x0=[1;0];xd0=[0;0];tf=50;dt=0.1;
/ Z) c% y) }/ ^7 \; Y. wM=[m1,0;0,m2];k=[k1+k2,-k2;-k2,k2];, ^$ u5 p1 b# \* w( V# k# v4 y
c=[c1+c2,-c2;-c2,c2];
5 m5 o4 m; Y6 j# ~( |4 L' X6 j4 IA=[zeros(2,2),eye(2);-M\k,-M\c];# |. m7 U& l; y/ S. Z
y0=[x0;xd0];
# C, X8 x( h$ O# g6 f" R1 ofor i=1:round(tf/dt)+1
6 ~8 h$ X8 }# v2 R+ ^ B/ X t(i)=dt*(i-1)
4 m; B1 h/ h/ i9 r6 h& M* P9 A y(:,i)=expm(A*t(i))*y0;
! Y) b- {$ m% nend
g- q! A8 L$ F* E9 W9 {subplot(2,1,1),plot(t,y(1, ),grid
& \' W( h* z7 f7 b/ P( @subplot(2,1,2),plot(t,y(2, ),grid8 {' k4 D) {" Q( ]$ k6 K8 {; d
[p,lamda]=eig(A)& c( [5 c. n' i* R/ E! m
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lamda =
2 x" C. U/ r1 W: o" j Columns 1 through 2
# ], v" @1 U3 o) C, y( F 0.000000000000000 + 3.020447918044219i 0.000000000000000 + 0.000000000000000i
/ F4 a4 `7 w2 y9 H: K/ W" X q 0.000000000000000 + 0.000000000000000i 0.000000000000000 - 3.020447918044219i
/ Q) U* B3 m5 n5 D/ x 0.000000000000000 + 0.000000000000000i 0.000000000000000 + 0.000000000000000i
! N2 U. n, H- g2 u" C- _; D 0.000000000000000 + 0.000000000000000i 0.000000000000000 + 0.000000000000000i
. g6 }; b$ v' k# G* v. X Columns 3 through 4
$ y6 k+ h7 t7 O# w( H2 z 0.000000000000000 + 0.000000000000000i 0.000000000000000 + 0.000000000000000i
6 g" p! Y$ i; B; U: ^ 0.000000000000000 + 0.000000000000000i 0.000000000000000 + 0.000000000000000i: W8 p0 v. r4 Y
-0.000000000000000 + 0.936426384924271i 0.000000000000000 + 0.000000000000000i% h/ h, J$ B/ k% {4 u
0.000000000000000 + 0.000000000000000i -0.000000000000000 - 0.936426384924271i( Q4 G" ~3 ?( r- `% m
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