% 无阻尼二自由系统固有频率的程序 20180401A
: m$ A# m; J, ^/ P/ em1=100;m2=100;k1=200;k2=400;% " z7 l/ s& g' Z2 P1 q; p0 x. ~
c1=0;c2=0;
) m; a T# H$ A! `; q/ {x0=[1;0];xd0=[0;0];tf=50;dt=0.1;/ I! a3 I4 ~6 Y+ h/ q$ ]
M=[m1,0;0,m2];k=[k1+k2,-k2;-k2,k2];
& v/ S& K3 ~; M; \( B- rc=[c1+c2,-c2;-c2,c2];
8 @# b1 k! |# w! j! wA=[zeros(2,2),eye(2);-M\k,-M\c];
( F0 `$ z9 s+ A4 m6 Fy0=[x0;xd0];
$ V1 \' Y" x8 @4 M( ]5 i1 } kfor i=1:round(tf/dt)+1
# _6 l# b1 u) V9 D9 i0 t t(i)=dt*(i-1)
5 _6 |8 N) [, r" O. N y(:,i)=expm(A*t(i))*y0;
% A/ o! g n( a- Q# y: Q7 s. p) gend# R {1 r. _- P/ K2 w$ s/ g( M1 a
subplot(2,1,1),plot(t,y(1,),grid $ G9 S! e: m K, v4 V$ U/ J7 z
subplot(2,1,2),plot(t,y(2,),grid; ~0 t" S1 M: `' O, o1 U/ h
[p,lamda]=eig(A)" L" H( } |4 x7 }' ?
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3 d l; C+ i8 o2 B W
# E- f, q3 H3 N$ N4 P0 wlamda =; D- d+ d3 G4 N9 \; U! G$ W
Columns 1 through 2
" u) c5 v/ I% z2 l1 F 0.000000000000000 + 3.020447918044219i 0.000000000000000 + 0.000000000000000i
" T9 h( [# @2 I7 d 0.000000000000000 + 0.000000000000000i 0.000000000000000 - 3.020447918044219i
9 G H' i% |$ c# X 0.000000000000000 + 0.000000000000000i 0.000000000000000 + 0.000000000000000i
8 F8 i& e9 O" G0 r( W 0.000000000000000 + 0.000000000000000i 0.000000000000000 + 0.000000000000000i
; H& g6 h) Y/ V; D+ E9 K7 e Columns 3 through 4: v% k8 q# M# o
0.000000000000000 + 0.000000000000000i 0.000000000000000 + 0.000000000000000i
5 l7 s" b/ ?+ M I. b 0.000000000000000 + 0.000000000000000i 0.000000000000000 + 0.000000000000000i
h+ |8 s4 e/ C -0.000000000000000 + 0.936426384924271i 0.000000000000000 + 0.000000000000000i
K- q$ t- E- T5 i5 E5 S 0.000000000000000 + 0.000000000000000i -0.000000000000000 - 0.936426384924271i" e9 a- _# t9 n) A) Q
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5 y) R! ^: V: m( l+ V
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