% 无阻尼二自由系统固有频率的程序 20180401A
3 k9 c2 }( p; R8 {7 {m1=100;m2=100;k1=200;k2=400;% 9 D. _7 E6 u9 P, u9 D
c1=0;c2=0;
$ G4 I7 @3 |: z8 U, A+ W& kx0=[1;0];xd0=[0;0];tf=50;dt=0.1;8 o* y/ w7 J- J# R' [& X
M=[m1,0;0,m2];k=[k1+k2,-k2;-k2,k2];
. [0 N8 ^5 r) }- `8 @c=[c1+c2,-c2;-c2,c2];5 W7 P! G0 j' j
A=[zeros(2,2),eye(2);-M\k,-M\c];
* Y7 D5 C. k) }' }y0=[x0;xd0];
+ x' l! R! k. w, ~0 o7 F5 ]% P- Efor i=1:round(tf/dt)+1
; D |5 T4 C$ C% _ t(i)=dt*(i-1)
( x- C0 k( ~9 r# B3 ^ H y(:,i)=expm(A*t(i))*y0;3 u3 F& E* w; M, D! E1 L
end
8 C9 D/ m3 k }/ Q7 Lsubplot(2,1,1),plot(t,y(1, ),grid * r8 p/ t5 w6 B1 D; M, B
subplot(2,1,2),plot(t,y(2,),grid N( y7 H% p4 @
[p,lamda]=eig(A)
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lamda =( \ [0 I# g6 s/ M: q" |# \2 c' Y
Columns 1 through 2; ^" _ e/ S' l, X* a: ]& z) F( J) F0 u
0.000000000000000 + 3.020447918044219i 0.000000000000000 + 0.000000000000000i( z2 l' `5 T0 q. W5 h" \) [
0.000000000000000 + 0.000000000000000i 0.000000000000000 - 3.020447918044219i1 O, D& D# W9 O Z1 X! y' q
0.000000000000000 + 0.000000000000000i 0.000000000000000 + 0.000000000000000i- b; k& ~5 w9 c ?2 p
0.000000000000000 + 0.000000000000000i 0.000000000000000 + 0.000000000000000i
* y$ [' r; Q- Y$ \ Columns 3 through 4
l6 X% [) l2 p0 m' h 0.000000000000000 + 0.000000000000000i 0.000000000000000 + 0.000000000000000i+ B0 h% K) q7 w& a! y9 j |
0.000000000000000 + 0.000000000000000i 0.000000000000000 + 0.000000000000000i. `* D3 A3 F- ^% N; l
-0.000000000000000 + 0.936426384924271i 0.000000000000000 + 0.000000000000000i
4 ?7 j! A0 C6 `* j$ }9 m% h3 e 0.000000000000000 + 0.000000000000000i -0.000000000000000 - 0.936426384924271i
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发表于 2018-4-16 19:41:12
