% 无阻尼二自由系统固有频率的程序 20180401A" f$ l! d( A& p
m1=100;m2=100;k1=200;k2=400;% ( F+ P- T. d* Q$ X
c1=0;c2=0;6 v6 x' J: C& B! s% b- f: ^
x0=[1;0];xd0=[0;0];tf=50;dt=0.1;
! [: f' h" E* b6 S+ @M=[m1,0;0,m2];k=[k1+k2,-k2;-k2,k2];
0 c- v" M4 q# N0 _& `7 `! d. qc=[c1+c2,-c2;-c2,c2];
2 A3 N1 e* ~# F; AA=[zeros(2,2),eye(2);-M\k,-M\c];
$ L; b, f5 o2 O2 F6 o$ W$ Y2 uy0=[x0;xd0];
- V# e! d! F2 O% o) D* ifor i=1:round(tf/dt)+1 C. x% B/ k2 f
t(i)=dt*(i-1)0 e) L) S$ B, }! v* G
y(:,i)=expm(A*t(i))*y0;* P! l3 q0 |3 t
end
0 \; S! [0 C+ \! Csubplot(2,1,1),plot(t,y(1, ),grid
* s5 H1 L5 |/ o: |* s+ q8 s6 msubplot(2,1,2),plot(t,y(2,),grid
5 |$ k5 Z* y4 x/ ~1 l[p,lamda]=eig(A). b( t) j' u0 S/ Y' Y
0 t% K! Y" J1 h' {$ \, E* i" o4 H" w: @
2 P6 u& n% {2 [6 [ U
3 C, N ?$ ~3 J9 V1 L9 y$ ulamda =' @& d. u# o7 E" O, `/ J
Columns 1 through 2% U: c' g: j- x Z
0.000000000000000 + 3.020447918044219i 0.000000000000000 + 0.000000000000000i5 H5 c0 | Q {' ]6 ~3 m& A
0.000000000000000 + 0.000000000000000i 0.000000000000000 - 3.020447918044219i
5 V% l7 ?2 f' G6 k1 W( z/ x 0.000000000000000 + 0.000000000000000i 0.000000000000000 + 0.000000000000000i! o+ X2 |. r& d' i# ]1 `
0.000000000000000 + 0.000000000000000i 0.000000000000000 + 0.000000000000000i3 ?5 p! d8 \ u' R# C/ k
Columns 3 through 4
( |8 k9 b( Y: j5 f8 n 0.000000000000000 + 0.000000000000000i 0.000000000000000 + 0.000000000000000i7 v6 X6 d% s h% {3 D& f& }
0.000000000000000 + 0.000000000000000i 0.000000000000000 + 0.000000000000000i2 J. G3 G0 H6 V' V) u4 |6 @% K
-0.000000000000000 + 0.936426384924271i 0.000000000000000 + 0.000000000000000i
( R4 P! q) J8 u2 Z, \7 t' R# A# F 0.000000000000000 + 0.000000000000000i -0.000000000000000 - 0.936426384924271i
1 H% h6 c$ _. a- G* y7 v4 U( l5 }- \+ U6 `5 w9 I2 }8 q
4 z! P+ @/ ~; c9 F. B$ L$ F0 i
% g: d6 Q- r2 V) T5 ?, b4 X# H+ b6 `2 a6 d2 b1 w; L
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发表于 2018-4-16 19:41:12
