% 无阻尼二自由系统固有频率的程序 20180401A7 s- q1 `8 l9 a* @" F6 L- G" n
m1=100;m2=100;k1=200;k2=400;%
# S- k( p! S6 N8 g3 v7 J+ q2 Mc1=0;c2=0;$ C# |9 F* F2 |) o1 t
x0=[1;0];xd0=[0;0];tf=50;dt=0.1;& f. |5 ]* C: d! }( C
M=[m1,0;0,m2];k=[k1+k2,-k2;-k2,k2];
5 l/ T, m: A: w. Mc=[c1+c2,-c2;-c2,c2];
: I m9 w+ B- E- z4 YA=[zeros(2,2),eye(2);-M\k,-M\c];
9 y- |% M, [. v- Y; w" Cy0=[x0;xd0];
0 p+ e3 @1 N( B% ]" S. K0 ufor i=1:round(tf/dt)+1! {, T: @; F4 @) `, E
t(i)=dt*(i-1)
7 P4 C1 }* q1 o! v- _ y(:,i)=expm(A*t(i))*y0;6 B+ x) j' `0 w9 T
end
* i! o9 j5 j( U- [subplot(2,1,1),plot(t,y(1, ),grid
& ]* e' N9 |) O) c7 t0 @' E: vsubplot(2,1,2),plot(t,y(2,),grid3 q- p8 I3 x. A
[p,lamda]=eig(A)
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# ^) }$ {$ q4 z( h
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lamda =
- N H1 ?/ l3 h( W Columns 1 through 2
. L" V6 E5 }( E* C& ^2 G8 Y" z 0.000000000000000 + 3.020447918044219i 0.000000000000000 + 0.000000000000000i8 J/ b2 Q! Q5 A
0.000000000000000 + 0.000000000000000i 0.000000000000000 - 3.020447918044219i
/ O3 b2 P* P* t% W 0.000000000000000 + 0.000000000000000i 0.000000000000000 + 0.000000000000000i
: p4 p- ~/ W9 W# [% f. M 0.000000000000000 + 0.000000000000000i 0.000000000000000 + 0.000000000000000i$ j8 J6 V" c$ F( d, u3 H1 F
Columns 3 through 4" Z; u4 F6 z6 w+ n
0.000000000000000 + 0.000000000000000i 0.000000000000000 + 0.000000000000000i' i& o0 R) R( v& @8 y
0.000000000000000 + 0.000000000000000i 0.000000000000000 + 0.000000000000000i1 y2 d0 L5 `- u% W& K9 @! b7 d
-0.000000000000000 + 0.936426384924271i 0.000000000000000 + 0.000000000000000i
( c* K7 n! c% R/ S/ ?" t 0.000000000000000 + 0.000000000000000i -0.000000000000000 - 0.936426384924271i/ J& S- B& j* K3 O
# q) _+ y; t" M. \6 \
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发表于 2018-4-16 19:41:12
