% 無阻尼二自由系統固有頻率的程序 20180401A
+ v2 z8 l3 F: B/ Q) r# e1 ym1=100;m2=100;k1=200;k2=400;% " q5 B7 x1 e- G
c1=0;c2=0;
: {+ [% Z& X' f2 K( @x0=[1;0];xd0=[0;0];tf=50;dt=0.1;9 w, o/ U5 V0 d1 o# ]
M=[m1,0;0,m2];k=[k1+k2,-k2;-k2,k2];
9 `% N; v. }9 jc=[c1+c2,-c2;-c2,c2];
. [3 X" ^6 T' [0 p# KA=[zeros(2,2),eye(2);-M\k,-M\c];
9 t% v* R: B7 ]+ h j( G' Oy0=[x0;xd0];5 P- ?; A8 p2 E
for i=1:round(tf/dt)+1& H0 d# }. o8 ]/ [1 {2 e$ `' m0 X
t(i)=dt*(i-1)& v5 v+ R* w9 n- J J K
y(:,i)=expm(A*t(i))*y0;) x- O1 E/ Y! {; U/ @5 Z# p) ~
end. b$ i$ |' Y9 o
subplot(2,1,1),plot(t,y(1, ),grid - w# v* v# E! c* R' A( n5 }
subplot(2,1,2),plot(t,y(2, ),grid
+ \3 A. |( N5 e- G! l[p,lamda]=eig(A). U, B I# \! v+ a- u- }1 p6 ^
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lamda =- ^6 I( B% J& f( A& {& q
Columns 1 through 2
1 f j6 t; i7 [5 j 0.000000000000000 + 3.020447918044219i 0.000000000000000 + 0.000000000000000i
$ v2 e) ~5 X2 S* R( o 0.000000000000000 + 0.000000000000000i 0.000000000000000 - 3.020447918044219i
- a/ z: O- p! i6 y# ]: r7 r$ v6 E# | 0.000000000000000 + 0.000000000000000i 0.000000000000000 + 0.000000000000000i
+ ]/ `1 ^/ b6 o( }% G% D! L 0.000000000000000 + 0.000000000000000i 0.000000000000000 + 0.000000000000000i
/ J" _3 l6 l& ^1 T( O Columns 3 through 4
' q. z1 l9 D1 \0 Y- ]5 n' p" r 0.000000000000000 + 0.000000000000000i 0.000000000000000 + 0.000000000000000i
4 n1 ?9 b4 G. Q1 c" l- ~7 w' \+ H 0.000000000000000 + 0.000000000000000i 0.000000000000000 + 0.000000000000000i
3 z3 U: r4 F& z# P, c! N+ g! C) z( Y -0.000000000000000 + 0.936426384924271i 0.000000000000000 + 0.000000000000000i5 ~2 U/ C/ ~; ~; s
0.000000000000000 + 0.000000000000000i -0.000000000000000 - 0.936426384924271i8 \* S3 n: w# p' `: ]% {
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