Ecuaciones Diferenciales Ordinarias
Ecuaciones Diferenciales Ordinarias
Ecuaciones Diferenciales Ordinarias
PRACTICA ENCARGADA # 03
PROBLEMA:
Cuando el cuerpo sujeto al resorte se mueve en un medio que produce friccin sobre el cuerpo,
entonces decimos que el movimiento se efecta con amortiguamiento, supongamos
que el
Dnde:
Resolver la EDO para los siguientes casos y reproducir las funciones mostradas. Asumir las
contantes necesarias para lograr los casos a, b y c.
a) Cuando
Pgina 1
b) Cuando
c) Cuando
Dnde: k > 0 es una constante llamada mdulo o constante del resorte S es el alargamiento del
resorte despus que la masa ha sido colgada y el sistema est en reposo en la posicin de
equilibrio.
Es decir: Si una masa se sujeta a un resorte lo alargar en una magnitud S y alcanzar la posicin
de equilibrio en la cual su peso w es equilibrado por la fuerza de restitucin k s
Pgina 2
Cuando el sistema est en movimiento, esto quiere decir que la masa se desplaza de su posicin
de equilibrio en una magnitud x y despus se suelta, la fuerza neta correspondiente est dada por
la segunda ley del movimiento de Newton.
F = m*a
Donde a es la aceleracin
Suponiendo que sobre el sistema no actan otras fuerzas exteriores (movimiento vibratorio libre) y
la masa oscila libre, entonces podemos igualar F a la resultante del peso y la fuerza de restitucin
obteniendo la Ecuacin Diferencial que representa el movimiento.
El signo negativo indica que la fuerza de restitucin del resorte acta en direccin opuesta a la del
movimiento. Los desplazamientos medidos hacia abajo desde la posicin de equilibrio se
considerarn positivos.
Dividiendo por la masa la ecuacin anterior, se obtiene
Donde
Pgina 3
Interpretacin Fsica
Si analizamos el signo, podemos interpretar su significado fsico
Si a < 0 y b > 0, se trata de una masa que parte de un punto bajo la posicin de equilibrio y
lleva una velocidad hacia arriba.
Si a < 0 y b = 0, se trata de una masa en reposo, que se suelta desde un punto | | unidades
arriba de la posicin de equilibrio.
Pgina 4
adems el perodo
Unidades
Pgina 5
Pgina 6
, las
Posible grafica
Datos de Entrada
h=
=
w=
Pgina 7
0.2
5
3
k1
l1
0.2
2.6562
-1.8
-0.36
0.4 2.23179948
-1.98744
0.6 1.84353926 1.77379906
0.8 1.51401639 1.49411254
1 1.24090261 1.23522205
1.2 1.01634703 -1.0147258
1.4 0.83222528 0.83176258
1.6 0.68140142 0.68126937
1.8 0.55789486 0.55785717
2 0.45676963 0.45675888
2.2 0.37397324 0.37397017
2.4 0.30618456 0.30618369
2.6 0.25068357 0.25068332
2.8 0.20524301 0.20524294
3 0.1680393 0.16803928
3.2 0.13757937
-
k2
k3
-0.54
-1.18116 -0.478116
-0.397488 0.04235906 0.40172391
0.35475981 0.22922746 0.33183707
0.29882251 0.26299557 0.27252295
0.24704441 0.2368194 0.22336247
0.20294516 0.20002694 0.18294247
0.16635252 0.16551966 0.14980055
0.13625387 0.13601618 0.12265226
0.11157143 0.1115036 0.10042107
0.09135178 0.09133241 0.08221853
0.07479403 0.07478851 0.06731518
0.06123674 0.06123516 0.05511322
0.05013666 0.05013621 0.04512304
0.04104859 0.04104846 0.03694374
0.03360786 0.03360782 0.03024707
- 0.02751586
-
0.324
Pgina 8
-5.4
l2
l3
0
k4
-4.914
0.3577392
-0.3276 -1.0748556
-0.36171408 0.03854675
0.31928383
-0.32283143 0.20859699
0.26894026
-0.27192848 0.23932597
0.22233997
-0.22481041 0.21550566
0.18265064
-0.1846801 0.18202452
0.14971726
-0.15138079 0.15062289
0.12262849
-0.12399102 0.12377472
0.10041429
-0.10153001 0.10146827
0.0822166
-0.08313012
0.0831125
0.06731463
-0.06806257 0.06805754
0.05511306
-0.05572543
0.045123
0.055724
-0.04562436 0.04562395
0.03694373
-0.03735421
0.0373541
0.03024707
0.02476429
-0.03058315 0.03058311
-0.02503945 0.02503944
-0.9828
0.57497112
0.40519735
0.31304041
0.25095731
0.20394328
0.16654026
0.13622794
0.11149893
0.09127778
0.07472928
0.06118253
0.05009194
0.04101187
0.03357777
0.02749123
-
l4
4.428
1.5582312
0.68581978
0.39313006
0.2738149
0.21046683
0.16840208
0.1367593
0.11165058
0.09132106
0.07474163
0.06118605
0.05009294
0.04101216
0.03357785
0.02749126
0.02250799
3.4
3.6
3.8
4
4.2
4.4
4.6
4.8
5
5.2
5.4
5.6
5.8
6
6.2
0.13757937
0.11264082
0.09222279
0.07550588
0.06181918
0.05061342
0.02751587
0.11264082
0.02252816
0.09222279
0.01844456
0.07550588
0.01510118
0.06181918
0.01236384
0.05061342
0.01012268
0.0414389 -0.0414389 0.00828778
0.0339274 -0.0339274 0.00678548
0.0277775 -0.0277775
0.02274236 0.02274236
0.01861993 0.01861993
0.01524476 0.01524476
0.01248139 0.01248139
0.01021893 0.01021893
0.00836658 0.00836658
-0.0055555
0.00454847
0.00372399
0.00304895
0.00249628
0.00204379
0.00167332
0.00685
0.02476429
0.02252816 0.02027535 0.02027535
0.01842804
-0.01678455 0.01678455
0.00828778
0.00678548
0.0055555
0.00454847
0.00372399
0.00304895
0.00249628
0.00204379
0.00167332
-0.007459
0.00610693
0.00499995
0.00409363
0.00335159
0.00274406
0.00224665
0.00183941
0.00150598
-0.00685
-0.00137
0.00137 -0.001233
6.4 0.00560832 0.00560832 0.00112166 0.00112166 -0.0010095
Pgina 9
-0.02050063 0.02050063
0.02250799
0.01842804
0.01508765
0.01235276
0.01011362
0.00828036
0.007459
0.00610693
-0.01374207 0.01374207
-0.01125109 0.01125109
-0.00921164 0.00921164
0.00499995
-0.0050555
0.00409363
-0.00413911
0.00335159
-0.00338883
0.00274406
-0.00277455
0.00224665
-0.00227161
0.00183941
-0.00185985
0.00150598
-0.00152272
0.001233
-0.0012467
0.0010095
-0.00102071
0.0050555 -0.0045444
0.00413911 0.00372065
0.00338883 0.00304622
0.00277455 0.00249404
0.00227161 0.00204196
0.00185985 0.00167182
0.00152272 0.00136877
0.0012467 0.00112066
0.00102071 0.00091752
0.01508765
0.01235276
0.01011362
0.00828036
0.0045444
0.00372065
0.00304622
0.00249404
0.00204196
0.00167182
0.00136877
0.00112066
0.00091752
Pgina 10
9.1583E-05
7.4982E-05
-7.5815E-05 7.5815E-05
-6.139E-05 6.139E-05
-5.0262E05 5.0262E-05
-4.1151E05 4.1151E-05
-3.3692E- 3.3692E-05
-6.2072E-05 6.2072E-05
0.000504 -0.0004536
0.00041264 0.00037138
0.00033785 0.00030406
0.00027661 0.00024894
0.00022647 0.00020382
0.00018542 0.00016687
0.00015181 0.00013662
0.00012429 0.00011186
-9.1583E0.00010176
05
-7.4982E8.3313E-05
05
6.8211E-05
5.5847E-05
4.5724E-05
3.7436E-05
0.0004536
0.00037138
0.00030406
0.00024894
0.00020382
0.00016687
0.00013662
0.00011186
-5.0821E-05 5.0821E-05
-4.1609E-05 4.1609E-05
-3.4066E-05 3.4066E-05
-6.815E-05
-5.5797E05
-4.5683E05
-3.7402E05
-3.0622E-
0.00075121
0.00061504
0.00050355
0.00041227
0.00033754
0.00027636
0.00022626
0.00018525
0.00015167
0.00012418
0.00010167
8.3239E-05
6.815E-05
5.5797E-05
4.5683E-05
3.7402E-05
3.0622E-05
10 0.00015325
10.2 0.00012547
10.4 0.00010273
10.6 8.4106E-05
10.8
6.886E-05
11 5.6378E-05
11.2 4.6159E-05
11.4 3.7792E-05
11.6 3.0941E-05
11.8 2.5333E-05
12 2.0741E-05
12.2 1.6981E-05
12.4 1.3903E-05
12.6 1.1383E-05
12.8 9.3195E-06
13 7.6302E-06
0.00018718
0.00015325
0.00012547
0.00010273
-8.4106E05
-6.886E-05
-5.6378E05
-4.6159E05
-3.7792E05
-3.0941E05
-2.5333E05
-2.0741E05
-1.6981E05
-1.3903E05
-1.1383E05
-9.3195E06
-7.6302E06
05
-3.065E-05
-2.5094E05
-2.0545E05
-1.6821E05
-1.3772E05
-1.1276E05
-9.2317E06
-7.5583E06
-6.1882E06
-5.0665E06
-4.1481E06
-3.3962E06
-2.7806E06
-2.2766E06
-1.8639E06
-1.526E-06
Pgina 11
3.065E-05
2.5094E-05
2.0545E-05
1.6821E-05
1.3772E-05
1.1276E-05
9.2317E-06
7.5583E-06
6.1882E-06
5.0665E-06
4.1481E-06
3.3962E-06
2.7806E-06
2.2766E-06
1.8639E-06
1.526E-06
05
-2.7585E05
-2.2585E05
-1.8491E05
-1.5139E05
-1.2395E05
-1.0148E05
-8.3085E06
-6.8025E06
-5.5694E06
-4.5599E06
-3.7333E06
-3.0566E06
-2.5025E06
-2.0489E06
-1.6775E06
-1.3734E06
2.7585E-05
-2.7891E-05 2.7891E-05
2.2585E-05
-2.2836E-05 2.2836E-05
1.8491E-05
-1.8696E-05 1.8696E-05
1.5139E-05
-1.5307E-05 1.5307E-05
1.2395E-05
-1.2533E-05 1.2533E-05
1.0148E-05
-1.0261E-05 1.0261E-05
8.3085E-06
-8.4009E-06 8.4009E-06
6.8025E-06
-6.8781E-06 6.8781E-06
5.5694E-06
-5.6313E-06 5.6313E-06
4.5599E-06
-4.6105E-06 4.6105E-06
3.7333E-06
-3.7748E-06 3.7748E-06
3.0566E-06
-3.0906E-06 3.0906E-06
2.5025E-06
-2.5303E-06 2.5303E-06
2.0489E-06
-2.0717E-06 2.0717E-06
1.6775E-06
-1.6961E-06 1.6961E-06
1.3734E-06
-1.3887E-06 1.3887E-06
05
-2.5072E05 2.5072E-05
-2.0527E05 2.0527E-05
-1.6806E05 1.6806E-05
-1.376E-05
-1.1266E05
-9.2234E06
-7.5515E06
-6.1827E06
-5.062E-06
-4.1444E06
-3.3932E06
-2.7781E06
-2.2745E06
-1.8622E06
-1.5247E06
-1.2483E06
1.376E-05
1.1266E-05
9.2234E-06
7.5515E-06
6.1827E-06
5.062E-06
4.1444E-06
3.3932E-06
2.7781E-06
2.2745E-06
1.8622E-06
1.5247E-06
1.2483E-06
13.2 6.2471E-06
13.4 5.1147E-06
13.6 4.1876E-06
13.8 3.4285E-06
14
2.807E-06
14.2 2.2982E-06
14.4 1.8816E-06
14.6 1.5405E-06
14.8 1.2613E-06
15 1.0327E-06
15.2 8.4548E-07
15.4 6.9222E-07
15.6 5.6674E-07
15.8 4.6401E-07
16
3.799E-07
16.2 3.1104E-07
16.4 2.5466E-07
-6.2471E06
-5.1147E06
-4.1876E06
-3.4285E06
-2.807E-06
-2.2982E06
-1.8816E06
-1.5405E06
-1.2613E06
-1.0327E06
-8.4548E07
-6.9222E07
-5.6674E07
-4.6401E07
-3.799E-07
-3.1104E07
-2.5466E-
-1.2494E06 1.2494E-06
-1.0229E06 1.0229E-06
-8.3751E07 8.3751E-07
-6.857E-07
-5.6141E07
-4.5964E07
-3.7632E07
-3.0811E07
-2.5226E07
-2.0653E07
6.857E-07
5.6141E-07
4.5964E-07
3.7632E-07
3.0811E-07
2.5226E-07
2.0653E-07
-1.691E-07 1.691E-07
-1.3844E07 1.3844E-07
-1.1335E07 1.1335E-07
-9.2802E08 9.2802E-08
-7.598E-08 7.598E-08
-6.2208E08 6.2208E-08
-5.0932E- 5.0932E-08
Pgina 12
-1.1245E06
-9.2064E07
-7.5376E07
-6.1713E07
-5.0527E07
-4.1368E07
-3.3869E07
1.1245E-06
-1.137E-06
1.137E-06
9.2064E-07
-9.3087E-07 9.3087E-07
7.5376E-07
-7.6214E-07 7.6214E-07
6.1713E-07
-6.2399E-07 6.2399E-07
5.0527E-07
-5.1088E-07 5.1088E-07
4.1368E-07
-4.1827E-07 4.1827E-07
3.3869E-07
-3.4245E-07 3.4245E-07
-2.773E-07 2.773E-07
-2.2703E07 2.2703E-07
-1.8588E07 1.8588E-07
-1.5219E07 1.5219E-07
-2.8038E-07 2.8038E-07
-1.246E-07
-1.0201E07
-8.3522E08
-6.8382E08
-5.5987E08
-4.5838E-
1.246E-07
-1.2598E-07 1.2598E-07
1.0201E-07
-1.0315E-07 1.0315E-07
8.3522E-08
-2.2956E-07 2.2956E-07
-1.8794E-07 1.8794E-07
-1.5388E-07 1.5388E-07
-8.445E-08
8.445E-08
6.8382E-08
-6.9142E-08 6.9142E-08
5.5987E-08
4.5838E-08
-5.6609E-08 5.6609E-08
-4.6348E-08 4.6348E-08
-1.022E-06 1.022E-06
-8.3676E07 8.3676E-07
-6.8509E07 6.8509E-07
-5.609E-07
-4.5923E07
-3.7599E07
-3.0783E07
-2.5203E07
-2.0635E07
-1.6894E07
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-7.5912E08
-6.2152E08
-5.0886E08
-4.1662E-
5.609E-07
4.5923E-07
3.7599E-07
3.0783E-07
2.5203E-07
2.0635E-07
1.6894E-07
1.3832E-07
1.1325E-07
9.2719E-08
7.5912E-08
6.2152E-08
5.0886E-08
4.1662E-08
07
16.6
2.085E-07
-2.085E-07
16.8
1.707E-07
-1.707E-07
-1.3976E07
-1.1443E07
-9.3685E08
-7.6703E08
-6.2799E08
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-3.4465E08
-2.8218E08
-2.3103E08
-1.8915E08
-1.5486E08
-1.2679E08
-1.0381E08
17 1.3976E-07
17.2 1.1443E-07
17.4 9.3685E-08
17.6 7.6703E-08
17.8 6.2799E-08
18 5.1416E-08
18.2 4.2096E-08
18.4 3.4465E-08
18.6 2.8218E-08
18.8 2.3103E-08
19 1.8915E-08
19.2 1.5486E-08
19.4 1.2679E-08
19.6 1.0381E-08
08
-4.1699E08
-3.4141E08
-2.7952E08
-2.2885E08
-1.8737E08
-1.5341E08
4.1699E-08
3.4141E-08
2.7952E-08
2.2885E-08
1.8737E-08
1.5341E-08
-1.256E-08 1.256E-08
-1.0283E08 1.0283E-08
-8.4192E09 8.4192E-09
-6.893E-09 6.893E-09
-5.6436E09 5.6436E-09
-4.6206E09 4.6206E-09
-3.783E-09 3.783E-09
-3.0973E09 3.0973E-09
-2.5359E09 2.5359E-09
-2.0762E09 2.0762E-09
Pgina 13
08
-3.7529E08
-3.0727E08
-2.5157E08
-2.0597E08
-1.6863E08
-1.3807E08
-1.1304E08
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-3.4047E09
-2.7876E09
-2.2823E09
-1.8686E09
08
3.7529E-08
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3.0727E-08
-3.1068E-08 3.1068E-08
2.5157E-08
-2.5436E-08 2.5436E-08
2.0597E-08
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1.6863E-08
-1.7051E-08 1.7051E-08
1.3807E-08
-1.396E-08
1.396E-08
1.1304E-08
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9.2548E-09
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7.5772E-09
-7.6614E-09 7.6614E-09
6.2037E-09
-6.2727E-09 6.2727E-09
5.0792E-09
-5.1356E-09 5.1356E-09
4.1585E-09
-4.2047E-09 4.2047E-09
3.4047E-09
-3.4425E-09 3.4425E-09
2.7876E-09
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2.2823E-09
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1.8686E-09
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1.872E-08
1.5327E-08
1.2549E-08
1.0274E-08
8.4116E-09
6.8869E-09
5.6385E-09
4.6164E-09
3.7796E-09
3.0945E-09
2.5336E-09
2.0743E-09
1.6983E-09
19.8 8.4992E-09
20 6.9586E-09
20.2 5.6972E-09
20.4 4.6645E-09
20.6
3.819E-09
20.8 3.1267E-09
21
2.56E-09
21.2 2.0959E-09
21.4
1.716E-09
21.6 1.4049E-09
21.8 1.1503E-09
22 9.4177E-10
22.2 7.7106E-10
22.4 6.3129E-10
22.6 5.1686E-10
22.8 4.2317E-10
23 3.4646E-10
-8.4992E09
-6.9586E09
-5.6972E09
-4.6645E09
-3.819E-09
-3.1267E09
-2.56E-09
-2.0959E09
-1.716E-09
-1.4049E09
-1.1503E09
-9.4177E10
-7.7106E10
-6.3129E10
-5.1686E10
-4.2317E10
-3.4646E-
-1.6998E09 1.6998E-09
-1.3917E09 1.3917E-09
-1.1394E09 1.1394E-09
-9.329E-10
9.329E-10
-7.638E-10 7.638E-10
-6.2535E10 6.2535E-10
-5.1199E10 5.1199E-10
-4.1919E10 4.1919E-10
-3.432E-10
-2.8099E10
-2.3006E10
-1.8835E10
-1.5421E10
-1.2626E10
-1.0337E10
-8.4634E11
-6.9293E-
Pgina 14
3.432E-10
2.8099E-10
2.3006E-10
1.8835E-10
1.5421E-10
1.2626E-10
1.0337E-10
8.4634E-11
6.9293E-11
-1.5299E09
-1.2525E09
-1.0255E09
-8.3961E10
-6.8742E10
-5.6281E10
-4.6079E10
-3.7727E10
-3.0888E10
-2.5289E10
-2.0705E10
-1.6952E10
-1.3879E10
-1.1363E10
-9.3035E11
-7.6171E11
-6.2364E-
1.5299E-09
-1.5469E-09 1.5469E-09
1.2525E-09
-1.2665E-09 1.2665E-09
1.0255E-09
-1.0369E-09 1.0369E-09
8.3961E-10
-8.4894E-10 8.4894E-10
6.8742E-10
-6.9506E-10 6.9506E-10
5.6281E-10
-5.6907E-10 5.6907E-10
4.6079E-10
-4.6591E-10 4.6591E-10
3.7727E-10
-3.8146E-10 3.8146E-10
3.0888E-10
-3.1231E-10 3.1231E-10
2.5289E-10
2.0705E-10
1.6952E-10
1.3879E-10
1.1363E-10
-2.557E-10
2.557E-10
-2.0935E-10 2.0935E-10
-1.714E-10
1.714E-10
-1.4033E-10 1.4033E-10
-1.149E-10
1.149E-10
9.3035E-11
-9.4069E-11 9.4069E-11
7.6171E-11
6.2364E-11
-7.7017E-11 7.7017E-11
-6.3056E-11 6.3056E-11
-1.3905E09
-1.1384E09
-9.3207E10
-7.6311E10
-6.2479E10
-5.1153E10
-4.1881E10
-3.4289E10
-2.8074E10
-2.2985E10
-1.8819E10
-1.5407E10
-1.2615E10
-1.0328E10
-8.4558E11
-6.9231E11
-5.6682E-
1.3905E-09
1.1384E-09
9.3207E-10
7.6311E-10
6.2479E-10
5.1153E-10
4.1881E-10
3.4289E-10
2.8074E-10
2.2985E-10
1.8819E-10
1.5407E-10
1.2615E-10
1.0328E-10
8.4558E-11
6.9231E-11
5.6682E-11
23.2 2.8366E-10
23.4 2.3224E-10
23.6 1.9015E-10
23.8 1.5568E-10
24 1.2746E-10
24.2 1.0435E-10
24.4 8.5439E-11
24.6 6.9952E-11
24.8 5.7272E-11
25
4.689E-11
10
-2.8366E10
-2.3224E10
-1.9015E10
-1.5568E10
-1.2746E10
-1.0435E10
-8.5439E11
-6.9952E11
-5.7272E11
-4.689E-11
11
-5.6732E11
-4.6449E11
-3.8029E11
-3.1136E11
-2.5492E11
-2.0871E11
-1.7088E11
5.6732E-11
4.6449E-11
3.8029E-11
3.1136E-11
2.5492E-11
2.0871E-11
1.7088E-11
-1.399E-11 1.399E-11
-1.1454E11 1.1454E-11
-9.3781E12 9.3781E-12
Pgina 15
11
-5.1059E11
-4.1804E11
-3.4226E11
-2.8022E11
-2.2943E11
-1.8784E11
-1.5379E11
-1.2591E11
-1.0309E11
-8.4403E12
5.1059E-11
-5.1626E-11 5.1626E-11
4.1804E-11
-4.2268E-11 4.2268E-11
3.4226E-11
-3.4606E-11 3.4606E-11
2.8022E-11
-2.8333E-11 2.8333E-11
2.2943E-11
-2.3198E-11 2.3198E-11
1.8784E-11
-1.8993E-11 1.8993E-11
1.5379E-11
-1.555E-11
1.555E-11
1.2591E-11
-1.2731E-11 1.2731E-11
1.0309E-11
-1.0423E-11 1.0423E-11
8.4403E-12
-8.534E-12
8.534E-12
11
-4.6407E11
-3.7995E11
-3.1108E11
-2.5469E11
-2.0852E11
-1.7072E11
-1.3978E11
-1.1444E11
-9.3697E12
-7.6712E12
4.6407E-11
3.7995E-11
3.1108E-11
2.5469E-11
2.0852E-11
1.7072E-11
1.3978E-11
1.1444E-11
9.3697E-12
7.6712E-12
Grafica Caso I
3.5
Desplazamiento (S)
2.5
1.5
0.5
0
0
10
15
Tiempo (t)
Pgina 16
20
25
30
Datos de Entrada
h=
=
w=
x
0
1
2
3
4
5
6
7
1
0.33333333
0.33333333
0.18518519
0.08641975
0.03703704
0.01508916
0.00594422
k1
0
l1
k2
-4
1.33333333 1.33333333
-4
2.22222222
1.03703704
0.44444444
0.18106996
0.07133059
0.02743484
0.88888889 0.88888889
0.44444444 0.44444444
0.19753086 0.19753086
0.08230453 0.08230453
0.03292181 0.03292181
0.01280293 0.01280293
Pgina 17
1
2
2
-2
0.66666667
0.22222222
0.07407407
0.02469136
0.00823045
0.00274348
0.00091449
l2
k3
l3
1.33333333
0.44444444 1.11111111
0.14814815 0.51851852
0.04938272 0.22222222
0.01646091 0.09053498
0.00548697 0.03566529
0.00182899 0.01371742
-8
5.33333333
2.66666667
1.18518519
0.49382716
0.19753086
0.07681756
0.02926383
k4
l4
-8
20
-4 9.33333333
1.77777778
4
0.74074074 1.62962963
-0.2962963 0.64197531
0.11522634 0.24691358
0.04389575 0.09327846
0.01646091 0.0347508
8 0.00228624
9 0.00086369
10 0.00032177
11 0.00011855
-4.3279E12
05
-1.5681E13
05
14
22
-5.645E-06
-2.0211E06
-7.2015E07
-2.5554E07
-9.0341E08
-3.1834E08
-1.1185E08
-3.9196E09
-1.3703E09
23
24
-4.78E-10
-1.6641E-
15
16
17
18
19
20
21
Pgina 18
0.01280293
0.00467408
0.00169351
0.00060966
0.00021827
7.7776E-05
2.7598E-05
9.7568E-06
3.4381E-06
1.208E-06
4.2331E-07
1.4799E-07
5.1623E-08
1.7973E-08
6.2458E-09
2.1669E-09
7.5063E-10
25
10
-5.7832E11 1.1802E-10 1.1802E-10
10
-2.4077E10 -2.3605E-12 4.7209E-12 1.2038E-10
10
-2.4549E10
10
-1.2747E10 2.5965E-10
Grafica Caso II
1.2
1
0.8
Desplazamiento (S)
0.6
0.4
0.2
0
0
10
15
-0.2
-0.4
-0.6
Tiempo (t)
Pgina 19
20
25
30
Datos de Entrada
h=
=
w=
x
0
k1
l1
0.5
3
5
k2
0
0
-12.5
-3.125
0.5 0.28385417 4.94791667 2.47395833 11.2955729 0.3499349
1 0.89870199 3.06667752 1.53333876 2.03374227 2.04177433
1.5 0.35184629 1.67551217 0.83775609 9.42461513 -1.5183977
2 0.43148482 3.25497571 1.62748785 4.37136689 0.53464613
2.5 0.52173518 0.80639431 0.40319715 4.10250681 1.42882386
3 0.01150217 1.85280733 0.92640366 -5.7021991 0.49914611
3.5 0.36996639 -1.7311934 -0.8655967 0.56900033 0.72334662
4 0.23761553 0.26617716 0.13308858 3.76872556 0.80909281
Pgina 20
l2
k3
6.25
9.81445313
10.6002384
0.52366798
7.98611565
4.57123562
2.93892335
5.1254792
1.05255915
l3
k4
l4
1.5625
-2.34375 -1.171875
-25
0.02034505 5.61319987 5.28055827 28.3894857
1.11672084 5.1730103 4.11984391 0.47372182
0.70683909 0.85087243 1.2631923 20.8127211
0.36904106 4.26626825 3.76062198 12.5571584
0.73961175 2.02921113 1.41780272 7.26002028
0.19167283 1.82584912 1.83932822 13.5756568
0.4157731 2.59830212 2.16474776 3.16674292
0.39622837 0.29073423 0.01227853 7.84937748
4.5 0.12012905
0.09902364
0.11236909
0.00192604
0.08241093
0.04968552
-0.0287696
0.05374244
Pgina 21
1.55700794 -7.1538104
0.97389512 1.23943456
0.52174894 5.93876177
1.02727932 2.78496703
0.25959387 2.56626862
0.58159413 3.60344681
0.54809426 0.37856038
0.08065543 2.36984023
-0.4461365 1.74241989
0.21821623 0.63291574
0.18720616 1.65164741
-0.2737493 0.56622382
0.03436025 0.84282293
0.17656201 0.93162509
0.13426627 0.03175496
0.04439688 0.69303356
0.12456065
-
0.01457133
0.26573374
0.0014926 0.04527564
0.00938448 0.04829841
0.00689523 0.00278899
0.00250923 0.03663731
0.00653888 0.02069169
0.00223914 0.01365586
0.00333831 0.02341916
0.00368745 0.00464493
Pgina 22
0.06519518
0.06196335
0.08552559
-0.0082227
-0.0567191
0.40658484
0.04511286 0.24890703
0.06206832 0.44813846
0.07107572 0.09784956
0.00080908 0.26325538
0.05187297 0.23388637
0.087053
Pgina 23
0.00099055 0.02839419
0.00590086 0.03055945
0.00437324 0.00158202
0.00155447 0.02306802
-0.0041243 0.01315393
0.00143268 0.00852022
0.00209297 0.01478804
-0.0023327 0.00300734
-6.6946E05 0.00882446
Desplazamiento (S)
0.5
10
15
-0.5
-1
Tiempo (S)
Pgina 24
20
25
30
Pgina 25
Pgina 26
Pgina 27
Pgina 28
Pgina 29