% 无阻尼二自由系统固有频率的程序 20180401A9 V- M& K$ L: L5 Q- I. G/ ^0 h
m1=100;m2=100;k1=200;k2=400;%
( \+ f$ E% c9 Nc1=0;c2=0;
- l! }. x7 Q: P: X, zx0=[1;0];xd0=[0;0];tf=50;dt=0.1;4 j1 {8 g0 c! B4 T+ i* B" \5 y
M=[m1,0;0,m2];k=[k1+k2,-k2;-k2,k2];8 }5 E8 t3 H. r% e5 X7 T! h
c=[c1+c2,-c2;-c2,c2];, e1 Y7 u; ~( P# O; ~6 L
A=[zeros(2,2),eye(2);-M\k,-M\c];0 E7 E3 I1 q: B X( p- D
y0=[x0;xd0];
. m: M+ i. j! D6 z. E. hfor i=1:round(tf/dt)+1
2 p& T* a' R. o, P5 j0 h t(i)=dt*(i-1)
- \& O1 d; Y3 e; R; ] y(:,i)=expm(A*t(i))*y0;
* U' c, [; o. `# F" G' r! M# {7 t# vend
& L& }. e/ m9 { z/ R$ t2 asubplot(2,1,1),plot(t,y(1, ),grid
* {: p5 a l, rsubplot(2,1,2),plot(t,y(2,),grid
! m$ [% j) Y4 i[p,lamda]=eig(A)& @+ B2 k% g7 X# ^6 j$ O
$ X8 D$ c6 v! A* c) K1 s
9 I N; F) Z) q0 p0 m; D- j
/ N3 y- v$ v8 y- X: Q; H
' }& D5 H# X" ?* }2 g J E" {9 llamda =0 U* p2 f, B6 k/ @
Columns 1 through 20 b o0 K" x1 E1 _+ q; {8 n
0.000000000000000 + 3.020447918044219i 0.000000000000000 + 0.000000000000000i
9 H7 C9 p* q6 p c$ i5 f* J2 M) O 0.000000000000000 + 0.000000000000000i 0.000000000000000 - 3.020447918044219i% t2 T0 U+ ]. e
0.000000000000000 + 0.000000000000000i 0.000000000000000 + 0.000000000000000i
2 V D! K. Y# ~) P9 O3 d6 R 0.000000000000000 + 0.000000000000000i 0.000000000000000 + 0.000000000000000i
; I8 Q2 o" o% Q& M Columns 3 through 4) a- L: @0 L9 C+ y' D
0.000000000000000 + 0.000000000000000i 0.000000000000000 + 0.000000000000000i+ [9 o( f# F' y* [6 @
0.000000000000000 + 0.000000000000000i 0.000000000000000 + 0.000000000000000i
( A% H( B, f4 }* k -0.000000000000000 + 0.936426384924271i 0.000000000000000 + 0.000000000000000i" |* D7 Q+ O* t+ z8 ]
0.000000000000000 + 0.000000000000000i -0.000000000000000 - 0.936426384924271i: [1 A- w5 ?7 q7 X/ O% F1 J, D9 Y
: g+ J/ i5 `5 g/ b5 Y j
9 \- K# |1 T4 n' c+ Y8 I7 @+ B) T: S
2 E0 I4 m* R8 Z4 t9 ], `/ Q3 N# p* b. b: N1 P) m6 k
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发表于 2018-4-16 19:41:12
