% 无阻尼二自由系统固有频率的程序 20180401A
Q, `, D) Q' s8 f/ Z* em1=100;m2=100;k1=200;k2=400;%
, n" N( _: ]( n' y& Nc1=0;c2=0;6 D/ t% ^1 q5 C+ o w& o5 @) t# d
x0=[1;0];xd0=[0;0];tf=50;dt=0.1;
+ c1 E( @0 b% ~2 Z. K3 s" i3 o. e% `M=[m1,0;0,m2];k=[k1+k2,-k2;-k2,k2];
/ ^, z% z( p$ z1 o) \7 qc=[c1+c2,-c2;-c2,c2];
* g9 Z# a% U: }& H. P, }A=[zeros(2,2),eye(2);-M\k,-M\c];" D: ^. r# ?" l1 } k
y0=[x0;xd0];: x& w7 ]2 k+ H/ G1 K! c% q
for i=1:round(tf/dt)+18 P4 \, Y1 {: P) _- C5 E
t(i)=dt*(i-1)- g8 h; \* z0 ^1 c
y(:,i)=expm(A*t(i))*y0;; [- C( j, H- E @: x" N$ r7 s# o
end
8 e; c- b2 `$ dsubplot(2,1,1),plot(t,y(1, ),grid
% u4 `0 ^% Y+ msubplot(2,1,2),plot(t,y(2, ),grid
. z7 U) F" t0 B5 P5 Z# l- h[p,lamda]=eig(A)
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lamda =7 l( s& f9 F; b) A
Columns 1 through 2
9 S: {# T) L9 \) A( d 0.000000000000000 + 3.020447918044219i 0.000000000000000 + 0.000000000000000i: K4 a; _1 M" f0 Q3 z+ l! S
0.000000000000000 + 0.000000000000000i 0.000000000000000 - 3.020447918044219i
+ S3 j8 B V0 O5 a 0.000000000000000 + 0.000000000000000i 0.000000000000000 + 0.000000000000000i; _! G+ i- z; H, |
0.000000000000000 + 0.000000000000000i 0.000000000000000 + 0.000000000000000i
7 F0 _$ D' D5 e+ m: ?% O$ e8 s( ^0 Z Columns 3 through 47 j6 Y) q- s( g, ^- h
0.000000000000000 + 0.000000000000000i 0.000000000000000 + 0.000000000000000i; P+ y$ X: g8 L1 T
0.000000000000000 + 0.000000000000000i 0.000000000000000 + 0.000000000000000i
7 c% g: V% s/ t$ S -0.000000000000000 + 0.936426384924271i 0.000000000000000 + 0.000000000000000i3 `1 F9 H6 j7 L" [& w
0.000000000000000 + 0.000000000000000i -0.000000000000000 - 0.936426384924271i
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k8 o# ]) ^" N5 g9 A+ u$ [
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