Co-So-Ky-Thuat-Dien__Bai-Tap-Chuong-5 - [Cuuduongthancong.com].Pdf

cơ sở kỹ thuật điện,dhbkhcm 5 1/ a/ Đặt 1 2 x x      ta có 1 2 dx x dt  (1) 2 1 1 12 0,04 0,004 1 2sin (2) d d x x x dt dt       (2)=> 2 1 1 1 12 0,04 0,004 2co d d x x x x dt dt    [.]

5.1/   x1   x2 a/ Đặt  0, 04 ta có : dx1  x2 dt (1) d2 d x1  0, 004 x1   2sin x1 (2) dt dt c om d2 d (2)=> 0, 04 x1  0, 004 x1  co x1x1 dt dt d (1)=> x1  x2 x1 dt x  x1  x1  x2 an ng th     x1   x1        50cos x1 0,1  x2   x2  d2 d 0, 04 x1 _ 0,004 x1  2 cos x1x1 dt dt co ng    x1  x2  0,04 x2  0,004x2  cos x1x1 du o 0, 04x2  0,04x1  2cos x1x1 u   x    x1           0,1  50 cos x1   x2   x  2 cu b/ equilibrium points (điểm cân bằng)  2sin    sin    30 f  0 180  30  150    300  d2 d 0,04 x1  0, 004 x1   3x1  dt dt     x1  x2 Tại   1500 CuuDuongThanCong.com https://fb.com/tailieudientucntt  d2 d 0,04 x1  0,004 x1  3x1  dt dt     x1  x2 5.2/ a/ Te   I  0, 2sin   0,1sin 2   Equilibrium points c om Tm Te  1   0, 2sin   0,1sin 2   sin   0,3sin 2  0, 4sin   6sin  cos   4sin   ng   00    48,19 co b/ V(x)=U(x)-Win th an u ( x)  Mgl sin  x U  x    Mgl cos   V ( x)   Mgl cos   3Mgl  0,1  0, cos   0, 05cos 2  cu u du o ng V     Mgl sin   3Mgl  0, 2sin   0,1sin     2V     Mgl cos   3Mgl  0, 2cos   0, 2cos 2    2V     stable   0   2V     unstable   48,19   c/ V    Mgl cos   3Mgl  0,1  0, cos   0,05cos 2   C d/ 5.3/ CuuDuongThanCong.com https://fb.com/tailieudientucntt W 'm 2  Ax i x f e  kx  Ax 2i  kx x    x  2k  Ai  fe b/ U  x  x2  Kx  U  x   K x V  x   U  x   W 'm c om  x2 3 K  Ax i 2 ng 5.4/ a/ co x3  x  an x    x  1 b/ Phương trình đặc trưng du o  x  C1e0,618t  C2e 1,62t ng th 2   1    0,618  2  1,62 x    0,5  C1  C2  0,5 u  x   0, 618C1  1, 62C2  cu C1  0,362  C2  0,138 x  t   0,362e0,618t  0,138e1,62t  Tại (1,0): Phương trình đặc trưng:  21  1    1,2  0,5  1,323 j x  t   e0,5t (C1 cos1,323t  C2 sin1,323t ) C1  0,5  C2  0,189 CuuDuongThanCong.com https://fb.com/tailieudientucntt 5.5/ 0,1 d2 d   0,5   4 cos  dt dt     0,1 v  0,5  cos  1  c om     x1     x2   40cos  5.6/ an cu x   K x  9i  u  x  xi  K   du o d 2x M  f e  K  x  x0  dt W 'm W 'm   x 2i x e f  Wx co dx di  x3 dt dt th  30i  18 x 2i ng  t ng V  t   30i  CuuDuongThanCong.com https://fb.com/tailieudientucntt