% 无阻尼二自由系统固有频率的程序 20180401A! z8 }9 z3 Q: ^* T$ M
m1=100;m2=100;k1=200;k2=400;% . `+ N4 F+ w; n) C. M7 F- h- I
c1=0;c2=0;, T7 y/ w2 S: y1 v
x0=[1;0];xd0=[0;0];tf=50;dt=0.1;" P# F* }% i: X0 U* n5 c
M=[m1,0;0,m2];k=[k1+k2,-k2;-k2,k2];
( L$ Y% r( t( r8 fc=[c1+c2,-c2;-c2,c2];8 X8 x6 i- d: W2 D2 ^
A=[zeros(2,2),eye(2);-M\k,-M\c]; i% P0 l+ [% n. R4 Y5 }) ~7 k# ^
y0=[x0;xd0];
% L# |1 v8 I3 a! ofor i=1:round(tf/dt)+13 P' t, ]( k7 Q! R0 ~
t(i)=dt*(i-1)/ n4 X/ ?" K2 F+ ~2 b4 U
y(:,i)=expm(A*t(i))*y0;& B1 D7 u; C; b1 o# ]/ D
end
, P5 l' {- @' ]" }; H7 V! z7 jsubplot(2,1,1),plot(t,y(1, ),grid
' \$ S/ x9 r% R: \+ Xsubplot(2,1,2),plot(t,y(2,),grid
; y' l+ V5 @9 `% i5 _2 `[p,lamda]=eig(A)* p" t: n0 _% t1 g1 c8 h9 p' ^
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lamda =7 R7 D! X' R# F) o9 z" H! Q. F# G" ^, |8 H
Columns 1 through 2
/ B$ v! c! m# c) _7 f" D 0.000000000000000 + 3.020447918044219i 0.000000000000000 + 0.000000000000000i
7 u3 j. ~8 J! k: I o 0.000000000000000 + 0.000000000000000i 0.000000000000000 - 3.020447918044219i
) t+ Y3 D K0 v5 v( J' e G 0.000000000000000 + 0.000000000000000i 0.000000000000000 + 0.000000000000000i
1 d' P9 f n3 [; i+ b3 H' @& v 0.000000000000000 + 0.000000000000000i 0.000000000000000 + 0.000000000000000i
& D9 o: r8 w4 Y- f. P+ P Columns 3 through 4
( m8 g% f# [) n2 X' [" L 0.000000000000000 + 0.000000000000000i 0.000000000000000 + 0.000000000000000i; [6 O4 d0 }) R- p( A$ w: E+ e
0.000000000000000 + 0.000000000000000i 0.000000000000000 + 0.000000000000000i6 c+ w# y5 \ ^: @/ _
-0.000000000000000 + 0.936426384924271i 0.000000000000000 + 0.000000000000000i
* y$ i5 p8 b( ~7 r, w0 j4 ~ 0.000000000000000 + 0.000000000000000i -0.000000000000000 - 0.936426384924271i2 Y3 J$ x2 s7 h& k1 V+ B; ?# x8 @
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发表于 2018-4-16 19:41:12
