% 無阻尼二自由系統固有頻率的程序 20180401A
& Q$ o5 ^0 J0 |1 y7 c1 Q, km1=100;m2=100;k1=200;k2=400;%
3 t. S) g& ?: \0 G* w3 P# ~$ Ec1=0;c2=0;. \' o4 f; _7 r8 D. ^$ g5 E
x0=[1;0];xd0=[0;0];tf=50;dt=0.1;! N% Y( I$ s. F
M=[m1,0;0,m2];k=[k1+k2,-k2;-k2,k2];6 ?9 ]( E0 v$ I4 x( a4 e* Q. |
c=[c1+c2,-c2;-c2,c2];' Z: t3 n& J- ]: }+ `
A=[zeros(2,2),eye(2);-M\k,-M\c];
) U9 {6 n! w4 d9 K, n4 z& Py0=[x0;xd0];* \7 l( I, s# c7 ~$ f8 W
for i=1:round(tf/dt)+10 o5 B. O( e" R2 I( [2 Y, m
t(i)=dt*(i-1)8 B4 D2 @& C' n- ^/ r$ L1 ]
y(:,i)=expm(A*t(i))*y0;
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subplot(2,1,1),plot(t,y(1, ),grid 4 }$ x9 T% y+ n4 D
subplot(2,1,2),plot(t,y(2,),grid
2 [% y- R E& l[p,lamda]=eig(A)% m. L2 X- R, N" I. u
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lamda =
$ e( R3 K- A, H! q Columns 1 through 2
$ U3 g6 `& h4 F" n 0.000000000000000 + 3.020447918044219i 0.000000000000000 + 0.000000000000000i
! E/ K- q' i. @( X9 d 0.000000000000000 + 0.000000000000000i 0.000000000000000 - 3.020447918044219i
) d0 G( p, g+ h' k' {2 M( Q 0.000000000000000 + 0.000000000000000i 0.000000000000000 + 0.000000000000000i/ `+ A% b" r4 L- T
0.000000000000000 + 0.000000000000000i 0.000000000000000 + 0.000000000000000i/ B1 E' T/ m; Z+ c7 T1 U
Columns 3 through 44 \3 b6 Y1 @" n$ G: y& L6 J2 R% g
0.000000000000000 + 0.000000000000000i 0.000000000000000 + 0.000000000000000i& [4 ~4 m, v9 f/ P
0.000000000000000 + 0.000000000000000i 0.000000000000000 + 0.000000000000000i8 I/ t- ?" K6 `4 f# _4 D6 A- x2 f
-0.000000000000000 + 0.936426384924271i 0.000000000000000 + 0.000000000000000i- J& t9 g! y# r! w, O V
0.000000000000000 + 0.000000000000000i -0.000000000000000 - 0.936426384924271i _1 j9 ^) I3 k1 A2 d
2 I* @9 A/ t( k3 U. I
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發表于 2018-4-16 19:41:12
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