Vibracion Libre Amortiguado y No Amortiguada Final

Propiedades

Amplitud Max. Desp.

0.3 1 5 33.69 ° 0.3606 0.3606

𝑡

�(𝑡)

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 3 3.1 3.2 3.3 3.4 3.5

0.30000 0.35916 0.33038 0.22072 0.05702 -0.12065 -0.26877 -0.35109 -0.34745 -0.25874 -0.10669 0.07149 0.23217 0.33600 0.35757 0.29159 0.15422 -0.02091 -0.19092 -0.31418 -0.36053 -0.31860 -0.19867 -0.03010 0.14584 0.28608 0.35627 0.33923 0.23914 0.08050 -0.09785 -0.25224 -0.34488 -0.35308 -0.27483 -0.12929

�(𝑡)=�(0) 𝑐𝑜𝑠 〖� _𝑛 𝑡 〗 +(�  ̇(0))/�_𝑛 𝑠𝑖𝑛 〖� _𝑛 𝑡 〗 �_0=√( 〖 〖�(0) 〗 ^2+[(�  ̇(0))/�_𝑛 ]^2 ) ;𝐴𝑚𝑝𝑙𝑖𝑡�𝑑 𝑑�𝑙 𝑀𝑜𝑣𝑖𝑚𝑖�𝑛𝑡𝑜

vibracion libre no amortiguada 0.4

0.2

u(t)

�(0) �  ̇(0) �_𝑛 ∅_𝑓𝑎𝑠�

0.0

0

1

2

3

4

5

-0.2

-0.4 t (tiempo)

6

7

8

9

3.6 3.7 3.8 3.9 4 4.1 4.2 4.3 4.4 4.5 4.6 4.7 4.8 4.9 5 5.1 5.2 5.3 5.4 5.5 5.6 5.7 5.8 5.9 6 6.1 6.2 6.3 6.4 6.5 6.6 6.7 6.8 6.9 7 7.1 7.2 7.3 7.4 7.5 7.6 7.7 7.8 7.9 8 8.1 8.2 8.3

0.04790 0.21336 0.32659 0.35985 0.30501 0.17550 0.00301 -0.17021 -0.30176 -0.35943 -0.32909 -0.21819 -0.05386 0.12365 0.27089 0.35181 0.34659 0.25651 0.10363 -0.07462 -0.23460 -0.33714 -0.35714 -0.28970 -0.15133 0.02409 0.19362 0.31574 0.36055 0.31709 0.19600 0.02692 -0.14875 -0.28801 -0.35674 -0.33814 -0.23674 -0.07739 0.10092 0.25451 0.34580 0.35242 0.27275 0.12631 -0.05106 -0.21593 -0.32793 -0.35964

8.4 8.5 8.6 8.7 8.8 8.9 9 9.1 9.2 9.3 9.4 9.5 9.6 9.7 9.8 9.9 10

-0.30330 -0.17270 0.00018 0.17302 0.30349 0.35966 0.32778 0.21564 0.05070 -0.12664 -0.27299 -0.35249 -0.34569 -0.25426 -0.10057 0.07774 0.23701

)/�_𝑛

)/�_𝑛 ]^2 )

e no amortiguada

5

tiempo)

6

7

8

9

10

Propiedades

Amplitud

0.3 1 0.05 5 4.99375 35.66 ° 0.36924

𝑡 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 3 3.1 3.2 3.3 3.4

�(𝑡) 0.30000 0.35740 0.32666 0.21940 0.06497 -0.09744 -0.22865 -0.29887 -0.29428 -0.21964 -0.09619 0.04422 0.16721 0.24428 0.25925 0.21157 0.11570 -0.00313 -0.11542 -0.19467 -0.22356 -0.19765 -0.12581 -0.02742 0.07271 0.15060 0.18872 0.17992 0.12857 0.04903 -0.03834 -0.11230 -0.15583 -0.16002 -0.12579

�(𝑡)=�^(−𝜉�_𝑛 𝑡) [�(0) 𝑐𝑜𝑠 〖� _𝐷 𝑡 〗 +(�  ̇(0)+𝜉�_𝑛 �(0))/�_𝐷 𝑠𝑖𝑛 〖� _𝐷 𝑡 〗 ] �_0=√( 〖� (0) 〗 ^2+[(�  (0)+𝜉�_𝑛 �(0))/�_𝐷 ]^2 ) ;𝐴𝑚𝑝𝑙𝑖𝑡�𝑑 𝑑�𝑙 𝑀𝑜𝑣𝑖𝑚𝑖�𝑛𝑡𝑜

vibración libre amortiguada 0.5

u(t)

�(0) �  ̇(0) 𝜉 �_𝑛 �_𝐷 ∅_𝑓𝑎𝑠�

0.0

0

2

4

6

8

10

-0.5 t (tiempo)

12

14

3.5 3.6 3.7 3.8 3.9 4 4.1 4.2 4.3 4.4 4.5 4.6 4.7 4.8 4.9 5 5.1 5.2 5.3 5.4 5.5 5.6 5.7 5.8 5.9 6 6.1 6.2 6.3 6.4 6.5 6.6 6.7 6.8 6.9 7 7.1 7.2 7.3 7.4 7.5 7.6 7.7 7.8 7.9 8 8.1 8.2

-0.06319 0.01144 0.07971 0.12561 0.13927 0.11901 0.07131 0.00891 -0.05257 -0.09851 -0.11867 -0.10952 -0.07465 -0.02366 0.03050 0.07473 0.09896 0.09837 0.07432 0.03370 -0.01300 -0.05431 -0.08063 -0.08642 -0.07129 -0.03987 -0.00046 0.03714 0.06403 0.07432 0.06636 0.04294 0.01041 -0.02302 -0.04933 -0.06257 -0.06022 -0.04360 -0.01739 0.01170 0.03658 0.05151 0.05341 0.04246 0.02190 -0.00288 -0.02577 -0.04138

8.3 8.4 8.5 8.6 8.7 8.8 8.9 9 9.1 9.2 9.3 9.4 9.5 9.6 9.7 9.8 9.9 10 10.1 10.2 10.3 10.4 10.5 10.6 10.7 10.8 10.9 11 11.1 11.2 11.3 11.4 11.5 11.6 11.7 11.8 11.9 12 12.1 12.2 12.3 12.4 12.5 12.6 12.7 12.8 12.9 13

-0.04636 -0.04002 -0.02443 -0.00377 0.01679 0.03233 0.03939 0.03670 0.02538 0.00855 -0.00950 -0.02441 -0.03275 -0.03287 -0.02513 -0.01177 0.00375 0.01762 0.02660 0.02880 0.02401 0.01372 0.00065 -0.01193 -0.02105 -0.02470 -0.02227 -0.01464 -0.00389 0.00727 0.01615 0.02073 0.02015 0.01478 0.00614 -0.00354 -0.01191 -0.01702 -0.01782 -0.01432 -0.00758 0.00065 0.00832 0.01363 0.01542 0.01345 0.00836 0.00152

13.1 13.2 13.3 13.4 13.5 13.6 13.7 13.8 13.9 14 14.1 14.2 14.3 14.4 14.5 14.6 14.7 14.8 14.9 15 15.1 15.2 15.3 15.4 15.5 15.6 15.7 15.8 15.9 16 16.1 16.2 16.3 16.4 16.5 16.6 16.7 16.8 16.9 17 17.1 17.2 17.3 17.4 17.5 17.6 17.7 17.8

-0.00535 -0.01060 -0.01307 -0.01230 -0.00862 -0.00307 0.00295 0.00796 0.01084 0.01098 0.00849 0.00410 -0.00106 -0.00571 -0.00877 -0.00959 -0.00808 -0.00471 -0.00038 0.00383 0.00692 0.00821 0.00747 0.00499 0.00144 -0.00229 -0.00528 -0.00687 -0.00674 -0.00500 -0.00216 0.00106 0.00387 0.00562 0.00594 0.00483 0.00262 -0.00011 -0.00268 -0.00449 -0.00513 -0.00452 -0.00286 -0.00059 0.00170 0.00348 0.00434 0.00412

17.9 18 18.1 18.2 18.3 18.4 18.5 18.6 18.7 18.8 18.9 19 19.1 19.2 19.3 19.4 19.5 19.6 19.7 19.8 19.9 20

0.00293 0.00110 -0.00091 -0.00260 -0.00358 -0.00367 -0.00287 -0.00143 0.00029 0.00185 0.00289 0.00319 0.00272 0.00162 0.00018 -0.00123 -0.00227 -0.00272 -0.00251 -0.00170 -0.00052 0.00072

� _𝐷 𝑡 〗 +(�  ̇(0)+𝜉�_𝑛

�_𝑛 �(0))/�_𝐷 ]^2 )

ón libre amortiguada

8

10

t (tiempo)

12

14

16

18

20

Propiedades

𝑡 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 3 3.1 3.2 3.3 3.4

�(𝑡)=�^(−𝜉�_𝑛 𝑡) [� �(0))/�_𝐷 𝑠𝑖𝑛 〖� _𝐷

1 0 0.05 5 4.99375

V.L.A �(𝑡) 1.00000 0.87959 0.55499 0.11368 -0.33325 -0.67880 -0.84539 -0.80197 -0.56914 -0.21174 0.17879 0.50757 0.69911 0.71435 0.55824 0.27644 -0.05764 -0.36166 -0.56449 -0.62261 -0.52921 -0.31398 -0.03427 0.23999 0.44356 0.53127 0.48783 0.33000 0.10107 -0.14084 -0.33731 -0.44365 -0.43885 -0.32948 -0.14676

�(𝑡)=�(0) 𝑐𝑜𝑠 〖� _ (�  ̇(0))/�_𝑛 𝑠𝑖𝑛 〖� _ V.L.N.A �(𝑡) 1.00000 0.87758 0.54030 0.07074 -0.41615 -0.80114 -0.98999 -0.93646 -0.65364 -0.21080 0.28366 0.70867 0.96017 0.97659 0.75390 0.34664 -0.14550 -0.60201 -0.91113 -0.99717 -0.83907 -0.47554 0.00443 0.48330 0.84385 0.99780 0.90745 0.59492 0.13674 -0.35492 -0.75969 -0.97845 -0.95766 -0.70240 -0.27516

Curvas Envolvente + 1.00125 -1.00125 0.97653 -0.97653 0.95242 -0.95242 0.92891 -0.92891 0.90597 -0.90597 0.88360 -0.88360 0.86179 -0.86179 0.84051 -0.84051 0.81976 -0.81976 0.79952 -0.79952 0.77978 -0.77978 0.76052 -0.76052 0.74175 -0.74175 0.72343 -0.72343 0.70557 -0.70557 0.68815 -0.68815 0.67116 -0.67116 0.65459 -0.65459 0.63843 -0.63843 0.62266 -0.62266 0.60729 -0.60729 0.59230 -0.59230 0.57767 -0.57767 0.56341 -0.56341 0.54950 -0.54950 0.53593 -0.53593 0.52270 -0.52270 0.50979 -0.50979 0.49721 -0.49721 0.48493 -0.48493 0.47296 -0.47296 0.46128 -0.46128 0.44989 -0.44989 0.43878 -0.43878 0.42795 -0.42795

1.2 1.0 0.8 0.6 0.4 0.2 u(t)

�(0) �  ̇(0) 𝜉 �_𝑛 �_𝐷

0.0 -0.2 -0.4 -0.6 -0.8 -1.0 -1.2

0

2

3.5 3.6 3.7 3.8 3.9 4 4.1 4.2 4.3 4.4 4.5 4.6 4.7 4.8 4.9 5 5.1 5.2 5.3 5.4 5.5 5.6 5.7 5.8 5.9 6 6.1 6.2 6.3 6.4 6.5 6.6 6.7 6.8 6.9 7 7.1 7.2 7.3 7.4 7.5 7.6 7.7 7.8 7.9 8 8.1 8.2

0.06210 0.24594 0.36208 0.38609 0.31672 0.17510 -0.00143 -0.16901 -0.28806 -0.33250 -0.29537 -0.18952 -0.04356 0.10568 0.22240 0.28032 0.26847 0.19308 0.07526 -0.05479 -0.16541 -0.23113 -0.23845 -0.18847 -0.09592 0.01503 0.11698 0.18602 0.20726 0.17798 0.10762 0.01499 -0.07670 -0.14561 -0.17637 -0.16352 -0.11224 -0.03666 0.04399 0.11020 0.14687 0.14667 0.11146 0.05134 -0.01810 -0.07984 -0.11949 -0.12868

0.21944 0.66032 0.93952 0.98870 0.79581 0.40808 -0.07956 -0.54773 -0.88179 -0.99996 -0.87330 -0.53283 -0.06191 0.42418 0.80641 0.99120 0.93332 0.64692 0.20214 -0.29214 -0.71489 -0.96261 -0.97465 -0.74806 -0.33832 0.15425 0.60906 0.91474 0.99647 0.83422 0.46773 -0.01328 -0.49103 -0.84857 -0.99835 -0.90369 -0.58778 -0.12796 0.36319 0.76541 0.98024 0.95507 0.69607 0.26664 -0.22807 -0.66694 -0.94252 -0.98734

0.41738 0.40708 0.39703 0.38723 0.37766 0.36834 0.35925 0.35038 0.34173 0.33329 0.32506 0.31703 0.30921 0.30157 0.29413 0.28686 0.27978 0.27287 0.26614 0.25956 0.25316 0.24691 0.24081 0.23486 0.22907 0.22341 0.21789 0.21251 0.20727 0.20215 0.19716 0.19229 0.18754 0.18291 0.17840 0.17399 0.16970 0.16551 0.16142 0.15743 0.15355 0.14976 0.14606 0.14245 0.13894 0.13550 0.13216 0.12890

-0.41738 -0.40708 -0.39703 -0.38723 -0.37766 -0.36834 -0.35925 -0.35038 -0.34173 -0.33329 -0.32506 -0.31703 -0.30921 -0.30157 -0.29413 -0.28686 -0.27978 -0.27287 -0.26614 -0.25956 -0.25316 -0.24691 -0.24081 -0.23486 -0.22907 -0.22341 -0.21789 -0.21251 -0.20727 -0.20215 -0.19716 -0.19229 -0.18754 -0.18291 -0.17840 -0.17399 -0.16970 -0.16551 -0.16142 -0.15743 -0.15355 -0.14976 -0.14606 -0.14245 -0.13894 -0.13550 -0.13216 -0.12890

8.3 8.4 8.5 8.6 8.7 8.8 8.9 9 9.1 9.2 9.3 9.4 9.5 9.6 9.7 9.8 9.9 10 10.1 10.2 10.3 10.4 10.5 10.6 10.7 10.8 10.9 11 11.1 11.2 11.3 11.4 11.5 11.6 11.7 11.8 11.9 12 12.1 12.2 12.3 12.4 12.5 12.6 12.7 12.8 12.9 13

-0.10669 -0.06029 -0.00176 0.05434 0.09473 0.11052 0.09915 0.06465 0.01640 -0.03342 -0.07282 -0.09291 -0.08984 -0.06546 -0.02663 0.01666 0.05386 0.07638 0.07957 0.06360 0.03321 -0.00362 -0.03779 -0.06127 -0.06897 -0.05983 -0.03684 -0.00618 0.02446 0.04777 0.05853 0.05479 0.03815 0.01320 -0.01368 -0.03598 -0.04860 -0.04900 -0.03768 -0.01791 0.00517 0.02589 0.03942 0.04287 0.03592 0.02073 0.00133 -0.01744

-0.79042 -0.39999 0.08838 0.55511 0.88593 0.99984 0.86896 0.52532 0.05307 -0.43218 -0.81161 -0.99234 -0.93010 -0.64014 -0.19346 0.30059 0.72105 0.96497 0.97263 0.74215 0.32998 -0.16299 -0.61605 -0.91828 -0.99569 -0.82931 -0.45989 0.02213 0.49873 0.85322 0.99882 0.89987 0.58060 0.11918 -0.37142 -0.77108 -0.98196 -0.95241 -0.68969 -0.25810 0.23668 0.67351 0.94544 0.98590 0.78497 0.39186 -0.09720 -0.56245

0.12571 0.12261 0.11958 0.11663 0.11375 0.11094 0.10820 0.10553 0.10293 0.10038 0.09791 0.09549 0.09313 0.09083 0.08859 0.08640 0.08427 0.08219 0.08016 0.07818 0.07625 0.07437 0.07253 0.07074 0.06899 0.06729 0.06563 0.06401 0.06243 0.06089 0.05938 0.05792 0.05649 0.05509 0.05373 0.05241 0.05111 0.04985 0.04862 0.04742 0.04625 0.04511 0.04399 0.04291 0.04185 0.04081 0.03981 0.03882

-0.12571 -0.12261 -0.11958 -0.11663 -0.11375 -0.11094 -0.10820 -0.10553 -0.10293 -0.10038 -0.09791 -0.09549 -0.09313 -0.09083 -0.08859 -0.08640 -0.08427 -0.08219 -0.08016 -0.07818 -0.07625 -0.07437 -0.07253 -0.07074 -0.06899 -0.06729 -0.06563 -0.06401 -0.06243 -0.06089 -0.05938 -0.05792 -0.05649 -0.05509 -0.05373 -0.05241 -0.05111 -0.04985 -0.04862 -0.04742 -0.04625 -0.04511 -0.04399 -0.04291 -0.04185 -0.04081 -0.03981 -0.03882

13.1 13.2 13.3 13.4 13.5 13.6 13.7 13.8 13.9 14 14.1 14.2 14.3 14.4 14.5 14.6 14.7 14.8 14.9 15 15.1 15.2 15.3 15.4 15.5 15.6 15.7 15.8 15.9 16 16.1 16.2 16.3 16.4 16.5 16.6 16.7 16.8 16.9 17 17.1 17.2 17.3 17.4 17.5 17.6 17.7 17.8

-0.03113 -0.03672 -0.03327 -0.02204 -0.00609 0.01053 0.02383 0.03079 0.03005 0.02218 0.00939 -0.00502 -0.01752 -0.02523 -0.02654 -0.02145 -0.01148 0.00074 0.01219 0.02017 0.02294 0.02010 0.01260 0.00245 -0.00779 -0.01566 -0.01942 -0.01835 -0.01295 -0.00473 0.00423 0.01174 0.01608 0.01637 0.01273 0.00623 -0.00143 -0.00839 -0.01300 -0.01428 -0.01209 -0.00712 -0.00069 0.00559 0.01023 0.01220 0.01116 0.00750

-0.89000 -0.99965 -0.86454 -0.51777 -0.04423 0.44014 0.81675 0.99339 0.92681 0.63332 0.18477 -0.30902 -0.72715 -0.96725 -0.97053 -0.73619 -0.32161 0.17172 0.62300 0.92175 0.99483 0.82433 0.45201 -0.03098 -0.50638 -0.85780 -0.99921 -0.89597 -0.57337 -0.11039 0.37962 0.77669 0.98359 0.94968 0.68325 0.24954 -0.24527 -0.68002 -0.94829 -0.98438 -0.77946 -0.38370 0.10600 0.56975 0.89400 0.99937 0.86006 0.51018

0.03786 0.03693 0.03602 0.03513 0.03426 0.03342 0.03259 0.03179 0.03100 0.03024 0.02949 0.02876 0.02805 0.02736 0.02668 0.02602 0.02538 0.02475 0.02414 0.02355 0.02297 0.02240 0.02185 0.02131 0.02078 0.02027 0.01977 0.01928 0.01880 0.01834 0.01789 0.01744 0.01701 0.01659 0.01618 0.01578 0.01539 0.01501 0.01464 0.01428 0.01393 0.01359 0.01325 0.01292 0.01260 0.01229 0.01199 0.01169

-0.03786 -0.03693 -0.03602 -0.03513 -0.03426 -0.03342 -0.03259 -0.03179 -0.03100 -0.03024 -0.02949 -0.02876 -0.02805 -0.02736 -0.02668 -0.02602 -0.02538 -0.02475 -0.02414 -0.02355 -0.02297 -0.02240 -0.02185 -0.02131 -0.02078 -0.02027 -0.01977 -0.01928 -0.01880 -0.01834 -0.01789 -0.01744 -0.01701 -0.01659 -0.01618 -0.01578 -0.01539 -0.01501 -0.01464 -0.01428 -0.01393 -0.01359 -0.01325 -0.01292 -0.01260 -0.01229 -0.01199 -0.01169

17.9 18 18.1 18.2 18.3 18.4 18.5 18.6 18.7 18.8 18.9 19 19.1 19.2 19.3 19.4 19.5 19.6 19.7 19.8 19.9 20

0.00224 -0.00331 -0.00779 -0.01020 -0.01005 -0.00751 -0.00330 0.00149 0.00570 0.00833 0.00885 0.00723 0.00396 -0.00009 -0.00393 -0.00664 -0.00763 -0.00675 -0.00430 -0.00095 0.00247 0.00513

0.03538 -0.44807 -0.82183 -0.99437 -0.92345 -0.62644 -0.17606 0.31743 0.73320 0.96946 0.96836 0.73017 0.31321 -0.18043 -0.62990 -0.92515 -0.99389 -0.81929 -0.44410 0.03982 0.51399 0.86232

0.01140 0.01112 0.01085 0.01058 0.01032 0.01006 0.00982 0.00957 0.00934 0.00911 0.00888 0.00866 0.00845 0.00824 0.00804 0.00784 0.00764 0.00746 0.00727 0.00709 0.00692 0.00675

-0.01140 -0.01112 -0.01085 -0.01058 -0.01032 -0.01006 -0.00982 -0.00957 -0.00934 -0.00911 -0.00888 -0.00866 -0.00845 -0.00824 -0.00804 -0.00784 -0.00764 -0.00746 -0.00727 -0.00709 -0.00692 -0.00675

�_0=√( 〖 〖�(0) 〗 ^2+[�  ̇(0)+(𝜉 ;𝐴𝑚𝑝𝑙𝑖𝑡�𝑑 𝑑�𝑙 𝑀𝑜𝑣𝑖𝑚𝑖�𝑛𝑡𝑜

�(𝑡)=�^(−𝜉�_𝑛 𝑡) [�(0) 𝑐𝑜𝑠 〖� _𝐷 𝑡 〗 +(� ( ̇ 0)+𝜉�_𝑛 �(0))/�_𝐷 𝑠𝑖𝑛 〖� _𝐷 𝑡 〗 ]

�(𝑡)=�(0) 𝑐𝑜𝑠 〖� _𝑛 𝑡 〗 + �  ̇(0))/�_𝑛 𝑠𝑖𝑛 〖� _𝑛 𝑡 〗

±�_0 �^(−𝜉�_𝑛 𝑡) ;𝐶�𝑟𝑣𝑎𝑠 𝐸𝑛𝑣𝑜𝑙𝑣

vibración libre amortiguada y no amortiguada 1.2 1.0 0.8 0.6 0.4

u(t)

0.2 0.0

0

2

4

6

8

10

12

14

16

-0.2 -0.4 -0.6 -0.8 -1.0 -1.2 t (tiempo) Vibración Amortiguada

Vibración No Amortiguada

Curva Envolvente +

Curva Envolvente -

18

�(0) 〗 ^2+[�  ̇(0)+(𝜉�_𝑛 �(0))/�_𝐷 ]^2 ) 𝑑�𝑙 𝑀𝑜𝑣𝑖𝑚𝑖�𝑛𝑡𝑜

_𝑛 𝑡) ;𝐶�𝑟𝑣𝑎𝑠 𝐸𝑛𝑣𝑜𝑙𝑣�𝑛𝑡�𝑠

16

Curva Envolvente -

18

20