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% 無(wú)阻尼二自由系統(tǒng)固有頻率的程序 20180401A
: ?, i8 Q, |- V7 ~m1=100;m2=100;k1=200;k2=400;%
% E$ R7 |5 C, rc1=0;c2=0;
2 t( k" H6 d& ^! C5 H) `. zx0=[1;0];xd0=[0;0];tf=50;dt=0.1;
6 x e- K$ ?/ t* XM=[m1,0;0,m2];k=[k1+k2,-k2;-k2,k2];; X9 b: L" w& m
c=[c1+c2,-c2;-c2,c2];! _3 a! l+ Z5 p3 {
A=[zeros(2,2),eye(2);-M\k,-M\c];
0 C5 T8 S/ s, p" hy0=[x0;xd0];
9 _ j0 o) Y- l4 a4 h& pfor i=1:round(tf/dt)+1: w* @5 u, X+ f$ l# l
t(i)=dt*(i-1)1 K" X: C" |; k* J
y(:,i)=expm(A*t(i))*y0;
6 F0 A, K) V8 t" s3 C$ [end; |3 M8 i8 T e' m
subplot(2,1,1),plot(t,y(1, ),grid - R5 _0 Q+ U2 i0 Z" v* d& E
subplot(2,1,2),plot(t,y(2, ),grid
; v4 \. B$ B5 v0 O* i[p,lamda]=eig(A), C; a: p4 G9 c, M) N
o3 |7 w' X7 i) l! f
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5 M9 s$ a& D( _$ [; C Q8 g/ J6 m. O- ]0 ^0 [
lamda =& }2 }. [1 v0 [$ ^* I
Columns 1 through 2
0 T& ~2 w, [7 u 0.000000000000000 + 3.020447918044219i 0.000000000000000 + 0.000000000000000i
( i: x+ Q. h5 t0 a; j( g) o3 A* f8 A3 S 0.000000000000000 + 0.000000000000000i 0.000000000000000 - 3.020447918044219i
7 {" W/ f2 F2 r6 ^4 X4 ~7 k2 I 0.000000000000000 + 0.000000000000000i 0.000000000000000 + 0.000000000000000i3 g# H5 I* Y. w) S
0.000000000000000 + 0.000000000000000i 0.000000000000000 + 0.000000000000000i
2 C' @2 z5 V6 N' ` Columns 3 through 4& N- c. |% R, o( Y
0.000000000000000 + 0.000000000000000i 0.000000000000000 + 0.000000000000000i" H- p4 f% d7 E2 _
0.000000000000000 + 0.000000000000000i 0.000000000000000 + 0.000000000000000i
% M( F, P/ u; ^9 j8 n" D# T- e7 @ -0.000000000000000 + 0.936426384924271i 0.000000000000000 + 0.000000000000000i- t9 t2 o+ k! F4 q& I8 G( K, Q) B
0.000000000000000 + 0.000000000000000i -0.000000000000000 - 0.936426384924271i
$ k& d3 q" U- E2 V9 q& F- A$ Y, V9 r$ j* K2 j3 k
) A2 H c; f) R7 M; K3 v2 e
, |9 y5 {; e2 ?/ C' ^6 }7 f8 S5 w3 i9 E! a
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