% 無阻尼二自由系統固有頻率的程序 20180401A
' O4 q3 R/ `2 M. q0 L+ Rm1=100;m2=100;k1=200;k2=400;% # m, k) }; C/ o+ }# u" |( N
c1=0;c2=0;
% S" ?4 l4 W/ D/ U5 R' s4 _x0=[1;0];xd0=[0;0];tf=50;dt=0.1;, G5 a2 F% c( O
M=[m1,0;0,m2];k=[k1+k2,-k2;-k2,k2];
# B: D6 V ^3 T9 Dc=[c1+c2,-c2;-c2,c2];
9 q; B. L- n0 A5 i& uA=[zeros(2,2),eye(2);-M\k,-M\c];6 _0 b* `) J7 {
y0=[x0;xd0];) [, f i8 J" r$ o2 N7 p
for i=1:round(tf/dt)+1
9 B* b$ `6 h$ v: o1 ]! m1 b t(i)=dt*(i-1)! D% B& T) V+ T, J1 X# T
y(:,i)=expm(A*t(i))*y0;
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subplot(2,1,1),plot(t,y(1, ),grid
$ W4 S4 g" `: X$ a4 Z' zsubplot(2,1,2),plot(t,y(2, ),grid
6 B X4 S! |: x: S2 x[p,lamda]=eig(A)
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8 A4 }" S& R( @: clamda =4 L# |! O4 I2 S7 b, {7 N
Columns 1 through 2' [/ n' J' @4 j, v4 y1 j- u( k$ `
0.000000000000000 + 3.020447918044219i 0.000000000000000 + 0.000000000000000i. I2 e* w, s4 `; w( m: R% O
0.000000000000000 + 0.000000000000000i 0.000000000000000 - 3.020447918044219i5 C; _0 T" T% u/ Y/ n" ]
0.000000000000000 + 0.000000000000000i 0.000000000000000 + 0.000000000000000i
$ _3 @* } }5 i0 r 0.000000000000000 + 0.000000000000000i 0.000000000000000 + 0.000000000000000i
. k% M1 {) O: d( u Columns 3 through 4 _% k; K6 j, g. R9 A/ ~
0.000000000000000 + 0.000000000000000i 0.000000000000000 + 0.000000000000000i( Y" ]% }% w3 r4 ^8 T: L' |
0.000000000000000 + 0.000000000000000i 0.000000000000000 + 0.000000000000000i) D6 i! K# q# ~' @) i; I
-0.000000000000000 + 0.936426384924271i 0.000000000000000 + 0.000000000000000i' u3 {( p: k$ U8 {; `
0.000000000000000 + 0.000000000000000i -0.000000000000000 - 0.936426384924271i+ B: t+ n1 D4 P$ Y' g w
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