% 无阻尼二自由系统固有频率的程序 20180401A. O3 i0 b n- M
m1=100;m2=100;k1=200;k2=400;%
- E$ V4 H$ d' h. Gc1=0;c2=0;& g7 K u! _6 K) V; F! M
x0=[1;0];xd0=[0;0];tf=50;dt=0.1;
, l; X2 D' Y% m( f1 D7 g5 fM=[m1,0;0,m2];k=[k1+k2,-k2;-k2,k2];7 U+ a, Q7 [6 G/ N9 J" n
c=[c1+c2,-c2;-c2,c2];0 E" J) _0 p- ?5 _( |6 Q, U9 b
A=[zeros(2,2),eye(2);-M\k,-M\c];9 h8 e; D; y( ^5 z
y0=[x0;xd0];
, c4 _- P% q& q t. ~0 `. w& i# cfor i=1:round(tf/dt)+1
5 k' a: P5 X' {9 n. u t(i)=dt*(i-1) Q9 n2 Q- U& V1 ], P! A4 G* s
y(:,i)=expm(A*t(i))*y0;. }- k: ?7 }# l; i) U; p
end
$ J* Y' v" i4 i: u! f- X, \* ssubplot(2,1,1),plot(t,y(1, ),grid 7 O8 F: r" k) K0 K
subplot(2,1,2),plot(t,y(2,),grid$ s- s+ C' O" B$ ^9 z
[p,lamda]=eig(A)
2 Q/ } A$ g( Z/ l% b: L& t8 P/ R1 T" P9 b, T8 x
1 a5 ?( `5 f& r2 l: `* I* J, d9 n2 r- f& `$ _
/ E7 f5 l% I h9 G$ v" D$ m3 S
lamda =+ Q O. d5 f9 C& _% T; o
Columns 1 through 2# x2 j6 A8 w6 S. @3 Y
0.000000000000000 + 3.020447918044219i 0.000000000000000 + 0.000000000000000i
& z$ L8 y$ x. ~) i' R4 h 0.000000000000000 + 0.000000000000000i 0.000000000000000 - 3.020447918044219i
. r3 T2 U- X9 N5 ]6 A; {1 K) w3 L+ x 0.000000000000000 + 0.000000000000000i 0.000000000000000 + 0.000000000000000i
( ?4 j( w T& v( O6 a( Z 0.000000000000000 + 0.000000000000000i 0.000000000000000 + 0.000000000000000i! x! H! ? {$ F' w4 E2 n5 p( @! x
Columns 3 through 49 k1 d7 _' P! t6 }
0.000000000000000 + 0.000000000000000i 0.000000000000000 + 0.000000000000000i' P9 f6 ]6 Y% ]( y
0.000000000000000 + 0.000000000000000i 0.000000000000000 + 0.000000000000000i7 d$ z( s; E L
-0.000000000000000 + 0.936426384924271i 0.000000000000000 + 0.000000000000000i
# {5 _ {4 L8 F' a0 h0 H# }: V' K" l 0.000000000000000 + 0.000000000000000i -0.000000000000000 - 0.936426384924271i4 N9 `+ W) _, ~6 i0 Q F# D
$ D2 w1 z- o1 ?3 {9 h1 w- U
2 `4 j9 l D4 a# S. o
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发表于 2018-4-16 19:41:12
