Pregunta1.xlsx

8/18/2019 Pregunta1.xlsx

1/74

DATOS:

0.05K = 20 Tn/m

10 rad/sg = 10 m/s2

Para

Asumir: masa = 1.8 Ton.s2/mPeso= 18 Ton

ω = 3.33 rad/s OK 3.0003.33 rad/s

C = 0.600 Ton.s/m

t X(t)0 0.0054679

0.01 -0.0015530.02 -0.0084740.03 -0.0152310.04 -0.0217670.05 -0.0280230.06 -0.0339460.07 -0.0394850.08 -0.0445920.09 -0.0492270.1 -0.053351

0.11 -0.0569330.12 -0.0599450.13 -0.0623670.14 -0.064184

0.15 -0.0653860.16 -0.0659720.17 -0.0659430.18 -0.065310.19 -0.0640870.2 -0.062295

0.21 -0.0599620.22 -0.057117

ξ =

ϖ =

β >>1

Hasta que ϖ>>ω

β =ωD =

0 0.5 1 1.5 2 2.5

-0.08

-0.06

-0.04

-0.02

0

0.02

0.040.06

0.08

t Vs X(t)

t s en K

t K

et X D

D

D

t ω β ω

ξ ϖ ξω ω β

ξω ]).)1(

)1(1010(cos.

)1(10

[)( 222

22 −

−+−

−=

−


2/74

0.23 -0.0537990.24 -0.0500470.25 -0.0459080.26 -0.0414290.27 -0.0366630.28 -0.031663

0.29 -0.0264870.3 -0.021191

0.31 -0.0158350.32 -0.0104760.33 -0.0051740.34 1.35"-0050.35 0.00503120.36 0.00982480.37 0.0143430.38 0.0185376

0.39 0.0223640.4 0.02578140.41 0.02875380.42 0.03124970.43 0.03324270.44 0.03471180.45 0.03564150.46 0.03602180.47 0.03584870.48 0.03512370.49 0.03385420.5 0.0320532

0.51 0.0297390.52 0.02693550.53 0.02367140.54 0.01998020.55 0.01589980.56 0.01147190.57 0.00674210.58 0.00175880.59 -0.0034270.6 -0.008762

0.61 -0.0141920.62 -0.019660.63 -0.0251110.64 -0.030490.65 -0.035740.66 -0.0408070.67 -0.04564


3/74

0.68 -0.0501890.69 -0.0544060.7 -0.058248

0.71 -0.0616750.72 -0.064650.73 -0.067142

0.74 -0.0691250.75 -0.0705760.76 -0.0714790.77 -0.0718220.78 -0.07160.79 -0.0708120.8 -0.069464

0.81 -0.0675660.82 -0.0651350.83 -0.06219

0.84 -0.0587590.85 -0.0548720.86 -0.0505630.87 -0.0458720.88 -0.0408420.89 -0.0355180.9 -0.029948

0.91 -0.0241840.92 -0.0182760.93 -0.012280.94 -0.0062480.95 -0.0002360.96 0.00570380.97 0.01151730.98 0.01715360.99 0.0225632

1 0.02769911.01 0.03251721.02 0.03697671.03 0.04104061.04 0.04467591.05 0.0478541.06 0.05055081.07 0.05274741.08 0.05442941.09 0.05558811.1 0.0562196

1.11 0.05632531.12 0.0559119


4/74

1.13 0.05499111.14 0.05357971.15 0.05169891.16 0.04937481.17 0.04663761.18 0.0435214

1.19 0.04006381.2 0.0363058

1.21 0.03229091.22 0.02806511.23 0.0236761.24 0.01917281.25 0.01460541.26 0.0100241.27 0.00547861.28 0.0010187

1.29 -0.0033071.3 -0.0074531.31 -0.0113751.32 -0.0150291.33 -0.0183781.34 -0.0213861.35 -0.024021.36 -0.0262541.37 -0.0280631.38 -0.0294281.39 -0.0303351.4 -0.030775

1.41 -0.0307421.42 -0.0302361.43 -0.0292631.44 -0.0278321.45 -0.0259591.46 -0.0236621.47 -0.0209651.48 -0.0178961.49 -0.0144861.5 -0.010769

1.51 -0.0067851.52 -0.0025731.53 0.00182191.54 0.00635631.55 0.01098311.56 0.0156551.57 0.0203241


5/74

1.58 0.02494251.59 0.02946281.6 0.0338386

1.61 0.03802491.62 0.04197841.63 0.0456584

1.64 0.04902671.65 0.05204821.66 0.05469121.67 0.05692771.68 0.05873391.69 0.06008991.7 0.0609805

1.71 0.06139481.72 0.06132681.73 0.0607751

1.74 0.05974281.75 0.0582381.76 0.05627311.77 0.05386511.78 0.05103531.79 0.04780871.8 0.0442144

1.81 0.04028491.82 0.03605591.83 0.03156561.84 0.02685511.85 0.0219671.86 0.01694571.87 0.01183671.88 0.00668621.89 0.00154051.9 -0.003554

1.91 -0.0085521.92 -0.013411.93 -0.0180841.94 -0.0225351.95 -0.0267221.96 -0.0306121.97 -0.0341721.98 -0.0373711.99 -0.040186

2 -0.0425952.01 -0.0445792.02 -0.046127


6/74

2.03 -0.0472292.04 -0.0478812.05 -0.0480832.06 -0.0478392.07 -0.0471592.08 -0.046056

2.09 -0.0445472.1 -0.042654

2.11 -0.0404012.12 -0.0378162.13 -0.0349322.14 -0.0317822.15 -0.0284032.16 -0.0248342.17 -0.0211162.18 -0.017289

2.19 -0.0133972.2 -0.0094832.21 -0.0055882.22 -0.0017572.23 0.00197042.24 0.00555322.25 0.00895332.26 0.0121342.27 0.01506162.28 0.01770482.29 0.02003552.3 0.0220292

2.31 0.02366472.32 0.02492462.33 0.02579562.34 0.02626852.35 0.02633822.36 0.02600372.37 0.02526832.38 0.02413962.39 0.0226292.4 0.0207519

2.41 0.01852762.42 0.01597892.43 0.01313182.44 0.01001562.45 0.00666212.46 0.00310572.47 -0.000617


7/74

2.48 -0.0044692.49 -0.0084092.5 -0.012398

2.51 -0.0163942.52 -0.0203582.53 -0.024247

2.54 -0.0280232.55 -0.0316462.56 -0.0350792.57 -0.0382872.58 -0.0412362.59 -0.0438962.6 -0.046239

2.61 -0.048242.62 -0.0498782.63 -0.051136

2.64 -0.0519982.65 -0.0524552.66 -0.0525012.67 -0.0521332.68 -0.0513542.69 -0.0501692.7 -0.048587

2.71 -0.0466232.72 -0.0442942.73 -0.0416192.74 -0.0386252.75 -0.0353362.76 -0.0317832.77 -0.0279992.78 -0.0240182.79 -0.0198762.8 -0.01561

2.81 -0.011262.82 -0.0068652.83 -0.0024632.84 0.00190442.85 0.00619932.86 0.01038332.87 0.01441952.88 0.01827282.89 0.02190982.9 0.0252995

2.91 0.02841362.92 0.0312263


8/74

2.93 0.03371522.94 0.03586112.95 0.03764822.96 0.03906442.97 0.04010132.98 0.0407542

2.99 0.04102233 0.0409086


9/74

Para

Asumir: masa = 0.01 Ton.s2/mPeso= 0.01 Ton

ω = 44. ! rad/s0.!!444.66 rad/s

C = 0.045 Ton.s/m

t X(t)0 0.5416315

0.01 0.46396760.02 0.30762260.03 0.11504260.04 -0.066770.05 -0.195560.06 -0.2417870.07 -0.1937990.08 -0.0593240.09 0.13684280.1 0.3583345

0.11 0.56471010.12 0.71941060.13 0.79663150.14 0.7858315

0.15 0.69311710.16 0.53936970.17 0.35561970.18 0.17667570.19 0.0343110.2 -0.048664

0.21 -0.0623450.22 -0.011014

β ""1

β =ωD =

3 3.5

X( !

0 0.5

-0.6

-0.4

-0.2

0

0.2

0.4

0.60.8

1

[ ]t t sen K

ϖ ξβ ϖ β β

cos2).1()1(

10 222

−−−

+


10/74

0.23 0.08836240.24 0.21000810.25 0.32474560.26 0.40581460.27 0.43397340.28 0.4009288

0.29 0.31050890.3 0.17745

0.31 0.0241360.32 -0.1239930.33 -0.2434240.34 -0.3169680.35 -0.3367530.36 -0.3052970.37 -0.2345430.38 -0.143126

0.39 -0.0524740.4 0.01744580.41 0.05191690.42 0.04407740.43 -0.0041020.44 -0.0825850.45 -0.1755650.46 -0.2647610.47 -0.3330630.48 -0.3677840.49 -0.3629290.5 -0.320075

0.51 -0.2477650.52 -0.1595810.53 -0.0713410.54 0.00201090.55 0.04921560.56 0.06466960.57 0.04922750.58 0.00972480.59 -0.0426280.6 -0.094619

0.61 -0.1336970.62 -0.1503740.63 -0.1399480.64 -0.1032190.65 -0.046110.66 0.02166840.67 0.0886424


11/74

0.68 0.14384030.69 0.17886930.7 0.189407

0.71 0.17584620.72 0.14300740.73 0.0990144

0.74 0.05358570.75 0.0160960.76 -0.0062090.77 -0.0095090.78 0.00601230.79 0.03638610.8 0.074796

0.81 0.11302450.82 0.14310660.83 0.1588632

0.84 0.1570250.85 0.13774760.86 0.10444650.87 0.06301190.88 0.02058230.89 -0.0158680.9 -0.04085

0.91 -0.0513350.92 -0.0472160.93 -0.0311880.94 -0.0080940.95 0.01611050.96 0.03556620.97 0.04563880.98 0.04376740.99 0.0298737

1 0.00627511.01 -0.022861.02 -0.0523921.03 -0.0772351.04 -0.0933341.05 -0.0983961.06 -0.0922531.07 -0.0768071.08 -0.0555711.09 -0.0329251.1 -0.013244

1.11 -5.5"-0051.12 0.004594


12/74

1.13 0.00046111.14 -0.0109291.15 -0.0266631.16 -0.0430641.17 -0.0564441.18 -0.063817

1.19 -0.0634511.2 -0.055153

1.21 -0.0402481.22 -0.0212641.23 -0.0013971.24 0.016121.25 0.02864151.26 0.03458091.27 0.03366681.28 0.0269315

1.29 0.01645151.3 0.00489751.31 -0.0050081.32 -0.011021.33 -0.0117851.34 -0.0070611.35 0.0022771.36 0.01446031.37 0.02720141.38 0.03815781.39 0.04538621.4 0.0476995

1.41 0.04486391.42 0.0376041.43 0.02742371.44 0.01628571.45 0.00621661.46 -0.0010821.47 -0.0045451.48 -0.0039151.49 0.00024611.5 0.0067036

1.51 0.01382191.52 0.01989991.53 0.02350421.54 0.02373731.55 0.02038921.56 0.01395171.57 0.0054956


13/74

1.58 -0.0035571.59 -0.0117211.6 -0.017732

1.61 -0.0207781.62 -0.0206351.63 -0.017684

1.64 -0.0128061.65 -0.0071931.66 -0.0021031.67 0.0013851.68 0.00257091.69 0.00125181.7 -0.002261

1.71 -0.0072251.72 -0.0126291.73 -0.0174

1.74 -0.0206131.75 -0.0216661.76 -0.0203781.77 -0.0170141.78 -0.0122081.79 -0.0068351.8 -0.001826

1.81 0.00200571.82 0.00411731.83 0.00432621.84 0.00282761.85 0.0001391.86 -0.0030161.87 -0.0058551.88 -0.0076951.89 -0.0080791.9 -0.006855

1.91 -0.0041931.92 -0.000541.93 0.00347571.94 0.00717641.95 0.00996291.96 0.01142761.97 0.01142391.98 0.01008251.99 0.0077738

2 0.00502652.01 0.00241892.02 0.0004655


14/74

2.03 -0.0004792.04 -0.0002792.05 0.00096362.06 0.00294122.07 0.00520972.08 0.0072803

2.09 0.00871562.1 0.0092134

2.11 0.00865882.12 0.00713962.13 0.0049212.14 0.0023882.15 -3.3"-0052.16 -0.0019572.17 -0.0031132.18 -0.003389

2.19 -0.0028452.2 -0.0016962.21 -0.0002612.22 0.00110342.23 0.00207292.24 0.00241762.25 0.00204222.26 0.00099932.27 -0.0005272.28 -0.0022642.29 -0.0039012.3 -0.005159

2.31 -0.0058342.32 -0.005842.33 -0.0052182.34 -0.0041192.35 -0.0027782.36 -0.0014592.37 -0.0004052.38 0.00020722.39 0.00029652.4 -0.000109

2.41 -0.0008842.42 -0.0018352.43 -0.0027412.44 -0.0033942.45 -0.0036462.46 -0.003432.47 -0.002769


15/74

2.48 -0.0017722.49 -0.0006092.5 0.0005285

2.51 0.00145872.52 0.00204812.53 0.0022326

2.54 0.00202752.55 0.001522.56 0.00084992.57 0.00017962.58 -0.0003382.59 -0.0005892.6 -0.000518

2.61 -0.0001382.62 0.00047842.63 0.0012114

2.64 0.00192212.65 0.0024792.66 0.00278322.67 0.00278622.68 0.00249692.69 0.00197792.7 0.001331

2.71 0.0006762.72 0.00012732.73 -0.0002282.74 -0.0003442.75 -0.0002262.76 7.60"-0052.77 0.00047852.78 0.00088122.79 0.00118782.8 0.0013248

2.81 0.00125452.82 0.0009812.83 0.00054782.84 2.79"-0052.85 -0.0004922.86 -0.0009272.87 -0.0012122.88 -0.0013122.89 -0.001232.9 -0.000998

2.91 -0.0006792.92 -0.000346


16/74

2.93 -7.0"-0052.94 9.22"-0052.95 0.00011082.96 -1.4"-0052.97 -0.0002542.98 -0.000557

2.99 -0.0008623 -0.001106


17/74

OK

Hasta que ϖ ω

1 1.5 2 2.5 3 3.5

t Vs X(t)

X( !


18/74


19/74


20/74


21/74


22/74


23/74


24/74


25/74

DATOS:

0.05K = 20 Tn/m

10 rad/sg = 10 m/s2

Para

Asumir: masa = 2 Ton.s2/mPeso= !0 Ton

ω = 3.1# rad/s OK 3.1#!

3.16 rad/sC = 0.632 Ton.s/m

t X(t)0 0.006172

0.01 0.00553490.02 0.00489420.03 0.00425070.04 0.00360490.05 0.00295760.06 0.00230940.07 0.0016610.08 0.00101290.09 0.00036590.1 -0.00028

0.11 -0.0009230.12 -0.0015630.13 -0.0021990.14 -0.0028310.15 -0.0034590.16 -0.0040810.17 -0.0046970.18 -0.0053060.19 -0.0059080.2 -0.006503

0.21 -0.0070890.22 -0.007666

ξ =

ϖ =

β >>1

Hasta que ϖ>>ω

β =ωD =

0 0.5 1 1.5 2 2.5

-0.025

-0.02

-0.015

-0.01

-0.005

0

0.0050.01

0.015

0.02

X(t)

).)1(

)1(1010(cos.

)1(10

[)( 222

22 se

K t

K et X

D

D

t

H

β ω ξ ϖ ξω

ω β

ξω

−

−+−

−=

−


26/74

0.23 -0.0082330.24 -0.0087910.25 -0.0093380.26 -0.0098740.27 -0.0103980.28 -0.010911

0.29 -0.0114110.3 -0.011898

0.31 -0.0123710.32 -0.0128310.33 -0.0132760.34 -0.0137070.35 -0.0141220.36 -0.0145230.37 -0.0149070.38 -0.015276

0.39 -0.0156280.4 -0.0159630.41 -0.0162810.42 -0.0165820.43 -0.0168660.44 -0.0171310.45 -0.0173790.46 -0.0176090.47 -0.017820.48 -0.0180130.49 -0.0181880.5 -0.018343

0.51 -0.018480.52 -0.0185980.53 -0.0186970.54 -0.0187770.55 -0.0188380.56 -0.018880.57 -0.0189040.58 -0.0189080.59 -0.0188930.6 -0.018859

0.61 -0.0188070.62 -0.0187360.63 -0.0186470.64 -0.0185390.65 -0.0184130.66 -0.0182690.67 -0.018108


27/74

0.68 -0.0179280.69 -0.0177320.7 -0.017518

0.71 -0.0172880.72 -0.0170410.73 -0.016778

0.74 -0.0164990.75 -0.0162040.76 -0.0158940.77 -0.0155690.78 -0.015230.79 -0.0148760.8 -0.014509

0.81 -0.0141280.82 -0.0137350.83 -0.013329

0.84 -0.0129110.85 -0.0124820.86 -0.0120410.87 -0.011590.88 -0.0111280.89 -0.0106570.9 -0.010177

0.91 -0.0096880.92 -0.0091910.93 -0.0086870.94 -0.0081750.95 -0.0076570.96 -0.0071330.97 -0.0066030.98 -0.0060690.99 -0.00553

1 -0.0049871.01 -0.0044411.02 -0.0038921.03 -0.0033411.04 -0.0027891.05 -0.0022351.06 -0.0016811.07 -0.0011271.08 -0.0005741.09 -2.2"-0051.1 0.0005284

1.11 0.00107661.12 0.0016219


28/74

1.13 0.00216391.14 0.0027021.15 0.00323581.16 0.00376461.17 0.00428791.18 0.0048054

1.19 0.00531641.2 0.0058205

1.21 0.00631721.22 0.0068061.23 0.00728641.24 0.00775811.25 0.00822061.26 0.00867341.27 0.0091161.28 0.0095482

1.29 0.00996951.3 0.01037951.31 0.01077791.32 0.01116421.33 0.01153821.34 0.01189951.35 0.01224771.36 0.01258261.37 0.01290391.38 0.01321131.39 0.01350461.4 0.0137834

1.41 0.01404761.42 0.0142971.43 0.01453131.44 0.01475031.45 0.01495391.46 0.0151421.47 0.01531431.48 0.01547081.49 0.01561141.5 0.0157359

1.51 0.01584431.52 0.01593661.53 0.01601271.54 0.01607251.55 0.01611611.56 0.01614351.57 0.0161547


29/74

1.58 0.01614971.59 0.01612871.6 0.0160915

1.61 0.01603851.62 0.01596961.63 0.0158849

1.64 0.01578471.65 0.01566911.66 0.01553811.67 0.01539211.68 0.01523111.69 0.01505551.7 0.0148654

1.71 0.0146611.72 0.01444271.73 0.0142106

1.74 0.01396511.75 0.01370641.76 0.01343491.77 0.01315081.78 0.01285441.79 0.01254621.8 0.0122264

1.81 0.01189541.82 0.01155361.83 0.01120141.84 0.0108391.85 0.0104671.86 0.01008571.87 0.00969561.88 0.0092971.89 0.00889041.9 0.0084762

1.91 0.00805481.92 0.00762681.93 0.00719241.94 0.00675231.95 0.00630681.96 0.00585641.97 0.00540161.98 0.00494291.99 0.0044806

2 0.00401542.01 0.00354762.02 0.0030777


30/74

2.03 0.00260632.04 0.00213372.05 0.00166062.06 0.00118722.07 0.00071422.08 0.0002419

2.09 -0.0002292.1 -0.000698

2.11 -0.0011662.12 -0.001632.13 -0.0020912.14 -0.0025492.15 -0.0030032.16 -0.0034522.17 -0.0038972.18 -0.004336

2.19 -0.004772.2 -0.0051972.21 -0.0056182.22 -0.0060322.23 -0.0064392.24 -0.0068382.25 -0.0072282.26 -0.0076112.27 -0.0079842.28 -0.0083492.29 -0.0087042.3 -0.009049

2.31 -0.0093842.32 -0.0097082.33 -0.0100222.34 -0.0103252.35 -0.0106162.36 -0.0108962.37 -0.0111652.38 -0.0114212.39 -0.0116652.4 -0.011897

2.41 -0.0121162.42 -0.0123222.43 -0.0125152.44 -0.0126962.45 -0.0128632.46 -0.0130162.47 -0.013156


31/74

2.48 -0.0132832.49 -0.0133962.5 -0.013495

2.51 -0.013582.52 -0.0136522.53 -0.01371

2.54 -0.0137532.55 -0.0137832.56 -0.01382.57 -0.0138022.58 -0.013792.59 -0.0137652.6 -0.013726

2.61 -0.0136742.62 -0.0136082.63 -0.013528

2.64 -0.0134362.65 -0.013332.66 -0.0132112.67 -0.013082.68 -0.0129362.69 -0.0127792.7 -0.01261

2.71 -0.0124292.72 -0.0122372.73 -0.0120322.74 -0.0118172.75 -0.011592.76 -0.0113522.77 -0.0111042.78 -0.0108452.79 -0.0105772.8 -0.010298

2.81 -0.0100112.82 -0.0097142.83 -0.0094082.84 -0.0090942.85 -0.0087722.86 -0.0084422.87 -0.0081052.88 -0.0077612.89 -0.007412.9 -0.007053

2.91 -0.006692.92 -0.006321


32/74

2.93 -0.0059482.94 -0.0055692.95 -0.0051862.96 -0.0047992.97 -0.0044092.98 -0.004015

2.99 -0.0036193 -0.00322


33/74

Para


ω = 44. ! rad/s0.!!4

44.66 rad/sC = 0.045 Ton.s/m

t X(t)0 0.5540202

0.01 0.42464010.02 0.21924570.03 -0.019330.04 -0.2437480.05 -0.4114620.06 -0.4926940.07 -0.4756060.08 -0.3677870.09 -0.1939450.1 0.0095932

0.11 0.2023790.12 0.3478020.13 0.41996410.14 0.40819140.15 0.31842150.16 0.17133420.17 -0.0022710.18 -0.1678420.19 -0.2938850.2 -0.357885

0.21 -0.3502480.22 -0.275577

β ""1

β =ωD =

3 3.5

X( !

0 0.5

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

]t Dω


34/74


35/74

0.68 0.08939610.69 0.11600920.7 0.1191443

0.71 0.09922560.72 0.06109340.73 0.012879

0.74 -0.0357030.75 -0.0752910.76 -0.0986650.77 -0.1020390.78 -0.0856390.79 -0.0534850.8 -0.01245

0.81 0.02918360.82 0.0633820.83 0.0838928

0.84 0.08736980.85 0.07388980.86 0.04678760.87 0.01187220.88 -0.0237990.89 -0.0533310.9 -0.071313

0.91 -0.0747920.92 -0.0637330.93 -0.0408990.94 -0.0111980.95 0.01935730.96 0.04485210.97 0.06060430.98 0.06401040.99 0.0549555

1 0.03572661.01 0.01046751.02 -0.01571.03 -0.0377021.04 -0.051491.05 -0.054771.06 -0.0473731.07 -0.0311871.08 -0.0097111.09 0.01269251.1 0.0316748

1.11 0.04373391.12 0.0468534


36/74

1.13 0.04082461.14 0.02720721.15 0.00895271.16 -0.0102251.17 -0.0265971.18 -0.037136

1.19 -0.0400721.2 -0.035171

1.21 -0.023721.22 -0.0082081.23 0.0082041.24 0.022321.25 0.03152511.26 0.03426381.27 0.03029231.28 0.0206681

1.29 0.00748971.3 -0.0065531.31 -0.018721.32 -0.0267541.33 -0.0292911.34 -0.0260831.35 -0.0179981.36 -0.0068061.37 0.00520621.38 0.0156911.39 0.02269891.4 0.0250342

1.41 0.02245211.42 0.01566461.43 0.00616111.44 -0.0041121.45 -0.0131441.46 -0.0192531.47 -0.0213911.48 -0.0193221.49 -0.0136261.5 -0.005559

1.51 0.0032241.52 0.01100281.53 0.01632481.54 0.0182741.55 0.01662311.56 0.0118471.57 0.0050013


37/74

1.58 -0.0025071.59 -0.0092041.6 -0.013838

1.61 -0.0156081.62 -0.0142981.63 -0.010295

1.64 -0.0044871.65 0.00192921.66 0.0076941.67 0.01172651.68 0.01332711.69 0.01229431.7 0.008942

1.71 0.00401641.72 -0.0014661.73 -0.006427

1.74 -0.0099341.75 -0.0113771.76 -0.0105691.77 -0.0077631.78 -0.0035871.79 0.00109641.8 0.0053639

1.81 0.0084131.82 0.00971041.83 0.00908341.84 0.00673661.85 0.00319691.86 -0.0008031.87 -0.0044731.88 -0.0071221.89 -0.0082861.9 -0.007805

1.91 -0.0058431.92 -0.0028441.93 0.00057131.94 0.00372711.95 0.00602791.96 0.00706871.97 0.00670421.98 0.00506631.99 0.0025255

2 -0.000392.01 -0.0031032.02 -0.0051


38/74

2.03 -0.0060292.04 -0.0057582.05 -0.0043912.06 -0.0022392.07 0.00024892.08 0.0025802

2.09 0.00431322.1 0.0051408

2.11 0.00494332.12 0.00380372.13 0.00198232.14 -0.0001412.15 -0.0021442.16 -0.0036472.17 -0.0043832.18 -0.004243

2.19 -0.0032942.2 -0.0017532.21 5.84"-0052.22 0.00177892.23 0.0030822.24 0.00373522.25 0.00364142.26 0.00285132.27 0.00154742.28 2.86"-0062.29 -0.0014752.3 -0.002604

2.31 -0.0031832.32 -0.0031242.33 -0.0024672.34 -0.0013652.35 -4.8"-0052.36 0.00122082.37 0.00219892.38 0.00271132.39 0.00267982.4 0.0021341

2.41 0.00120192.42 7.93"-0052.43 -0.0010092.44 -0.0018562.45 -0.0023092.46 -0.0022982.47 -0.001845


39/74

2.48 -0.0010582.49 -0.0001012.5 0.0008334

2.51 0.00156652.52 0.00196622.53 0.0019702

2.54 0.00159512.55 0.00092962.56 0.00011442.57 -0.0006872.58 -0.0013212.59 -0.0016742.6 -0.001689

2.61 -0.0013782.62 -0.0008162.63 -0.000122

2.64 0.00056552.65 0.00111412.66 0.00142442.67 0.00144722.68 0.00119052.69 0.00071622.7 0.0001248

2.71 -0.0004652.72 -0.0009392.73 -0.0012122.74 -0.001242.75 -0.0010282.76 -0.0006282.77 -0.0001242.78 0.00038112.79 0.0007912.8 0.0010309

2.81 0.0010622.82 0.00088742.83 0.00054982.84 0.00012132.85 -0.0003122.86 -0.0006662.87 -0.0008772.88 -0.0009092.89 -0.0007662.9 -0.000481

2.91 -0.0001162.92 0.0002547


40/74

2.93 0.00056062.94 0.00074532.95 0.00077862.96 0.00066072.97 0.00042082.98 0.0001105

2.99 -0.0002073 -0.000472


41/74

OK

Hasta que ϖ ω

1 1.5 2 2.5 3 3.5

X(t)

X( !


42/74


43/74


44/74


45/74


46/74


47/74


48/74


49/74

DATOS:

0.05K = 20 Tn/m

10 rad/sg = 10 m/s2

Para

Asumir: masa = 2 Ton.s2/mPeso= !0 Ton

ω = 3.1# rad/s OK 3.1#!

3.16 rad/sC = 0.632 Ton.s/m

t X$(t)0 -0.001952

0.01 -0.0074880.02 -0.0129490.03 -0.0182810.04 -0.0234310.05 -0.0283460.06 -0.0329780.07 -0.037280.08 -0.041210.09 -0.0447280.1 -0.0478

0.11 -0.0503940.12 -0.0524840.13 -0.054050.14 -0.0550750.15 -0.0555510.16 -0.0554710.17 -0.0548370.18 -0.0536560.19 -0.0519380.2 -0.049701

0.21 -0.0469670.22 -0.043765

ξ =

ϖ =

β >>1

Hasta que ϖ>>ω

β =ωD =

0 0.5 1 1.5 2 2.5

-0.08

-0.06

-0.04

-0.02

0

0.020.04

0.06

0.08

X$(t)

[ ]t t sen K

t X P ϖ ξβ ϖ β

β co s2).1(

)1(10

)( 222 −−−=


50/74


51/74


52/74

1.13 0.05241241.14 0.05030231.15 0.04768961.16 0.04460041.17 0.04106561.18 0.0371204

1.19 0.03280441.2 0.0281605

1.21 0.02323541.22 0.0180781.23 0.012741.24 0.00727471.25 0.00173681.26 -0.0038191.27 -0.0093361.28 -0.01476

1.29 -0.0200361.3 -0.0251121.31 -0.0299381.32 -0.0344641.33 -0.0386461.34 -0.0424411.35 -0.0458131.36 -0.0487271.37 -0.0511541.38 -0.053071.39 -0.0544551.4 -0.055297

1.41 -0.0555861.42 -0.055321.43 -0.0545011.44 -0.0531371.45 -0.0512421.46 -0.0488361.47 -0.0459411.48 -0.0425881.49 -0.0388091.5 -0.034642

1.51 -0.0301291.52 -0.0253151.53 -0.0202481.54 -0.0149791.55 -0.009561.56 -0.0040451.57 0.0015094


53/74

1.58 0.00704911.59 0.01251851.6 0.0178627

1.61 0.02302851.62 0.02796421.63 0.0326204

1.64 0.03695081.65 0.04091191.66 0.04446431.67 0.04757241.68 0.05020511.69 0.05233621.7 0.0539444

1.71 0.05501361.72 0.05553321.73 0.0554978

1.74 0.0549081.75 0.05376951.76 0.05209371.77 0.04989751.78 0.04720271.79 0.04403631.8 0.0404299

1.81 0.03641951.82 0.03204521.83 0.02735081.84 0.0223831.85 0.01719161.86 0.01182851.87 0.00634711.88 0.00080241.89 -0.004751.9 -0.010256

1.91 -0.0156591.92 -0.0209051.93 -0.0259421.94 -0.0307211.95 -0.0351921.96 -0.0393121.97 -0.0430391.98 -0.0463361.99 -0.04917

2 -0.0515122.01 -0.053342.02 -0.054635


54/74

2.03 -0.0553842.04 -0.055582.05 -0.055222.06 -0.0543092.07 -0.0528552.08 -0.050873

2.09 -0.0483832.1 -0.045409

2.11 -0.0419812.12 -0.0381342.13 -0.0339062.14 -0.0293392.15 -0.0244792.16 -0.0193752.17 -0.0140772.18 -0.008638

2.19 -0.0031132.2 0.00244342.21 0.00797522.22 0.01342732.23 0.01874522.24 0.02387592.25 0.0287682.26 0.03337262.27 0.03764382.28 0.04153882.29 0.04501892.3 0.0480491

2.31 0.05059922.32 0.05264372.33 0.05416232.34 0.05513962.35 0.05556612.36 0.05543732.37 0.05475472.38 0.05352492.39 0.05176032.4 0.0494786

2.41 0.04670252.42 0.04345972.43 0.03978282.44 0.03570832.45 0.0312772.46 0.02653322.47 0.0215244


55/74

2.48 0.01630042.49 0.01091362.5 0.0054177

2.51 -0.0001322.52 -0.0056812.53 -0.011173

2.54 -0.0165532.55 -0.0217682.56 -0.0267652.57 -0.0314952.58 -0.0359112.59 -0.0399672.6 -0.043624

2.61 -0.0468452.62 -0.0495992.63 -0.051856

2.64 -0.0535962.65 -0.05482.66 -0.0554562.67 -0.0555582.68 -0.0551062.69 -0.0541022.7 -0.052558

2.71 -0.0504892.72 -0.0479162.73 -0.0448632.74 -0.0413632.75 -0.0374492.76 -0.0331612.77 -0.0285412.78 -0.0236372.79 -0.0184962.8 -0.01317

2.81 -0.0077132.82 -0.0021792.83 0.00337682.84 0.0088992.85 0.01433242.86 0.01962252.87 0.02471652.88 0.02956362.89 0.03411532.9 0.0383261

2.91 0.0421542.92 0.0455607


56/74

2.93 0.04851222.94 0.05097892.95 0.05293632.96 0.05436482.97 0.05525012.98 0.0555833

2.99 0.05536123 0.0545859


57/74

Para


ω = 44. ! rad/s0.!!4

44.66 rad/sC = 0.045 Ton.s/m

t X$(t)0 -0.012389

0.01 0.04021730.02 0.09242140.03 0.14370210.04 0.1935470.05 0.2414580.06 0.28695640.07 0.32958770.08 0.36892580.09 0.40457770.1 0.4361873

0.11 0.46343860.12 0.48605930.13 0.50382360.14 0.51655370.15 0.52412270.16 0.52645480.17 0.52352670.18 0.51536780.19 0.50205940.2 0.4837346

0.21 0.46057650.22 0.4328165

β ""1

β =ωD =

3 3.5

X#( !

0 0.5

-0.6

-0.4

-0.2

0

0.2

0.4

0.6


58/74


59/74


60/74

1.13 -0.505831.14 -0.4887331.15 -0.4667531.16 -0.4401091.17 -0.4090681.18 -0.37394

1.19 -0.3350751.2 -0.292862

1.21 -0.2477231.22 -0.2001091.23 -0.1504951.24 -0.0993781.25 -0.0472681.26 0.00531481.27 0.05784421.28 0.1097956

1.29 0.160651.3 0.20989921.31 0.25705121.32 0.30163481.33 0.34320461.34 0.38134521.35 0.41567551.36 0.44585261.37 0.47157481.38 0.49258521.39 0.50867381.4 0.51968

1.41 0.52549371.42 0.52605681.43 0.52136371.44 0.51146131.45 0.49644861.46 0.47647561.47 0.45174171.48 0.42249421.49 0.38902531.5 0.3516694

1.51 0.31079971.52 0.26682451.53 0.22018341.54 0.17134231.55 0.12078921.56 0.06902911.57 0.0165794


61/74

1.58 -0.0360361.59 -0.0882911.6 -0.139664

1.61 -0.1896421.62 -0.2377251.63 -0.283432

1.64 -0.3263081.65 -0.3659231.66 -0.4018821.67 -0.4338261.68 -0.4614351.69 -0.4844331.7 -0.502591

1.71 -0.5157281.72 -0.5237111.73 -0.526462

1.74 -0.5239521.75 -0.5162081.76 -0.5033051.77 -0.4853741.78 -0.4625931.79 -0.435191.8 -0.403438

1.81 -0.3676561.82 -0.32821.83 -0.2854651.84 -0.2398771.85 -0.1918931.86 -0.1419911.87 -0.0906711.88 -0.0384451.89 0.01416551.9 0.0666343

1.91 0.11843731.92 0.1690571.93 0.21798751.94 0.26473991.95 0.30884711.96 0.34986851.97 0.38739411.98 0.42104891.99 0.4504968

2 0.47544352.01 0.49563962.02 0.5108836


62/74

2.03 0.52102292.04 0.52595642.05 0.52563462.06 0.52006092.07 0.5092912.08 0.4934323

2.09 0.47264352.1 0.4471321

2.11 0.41715322.12 0.38300622.13 0.34503232.14 0.3036112.15 0.25915612.16 0.21211172.17 0.16294812.18 0.1121563

2.19 0.06024392.2 0.00772962.21 -0.0448622.22 -0.0970052.23 -0.1481792.24 -0.1978732.25 -0.2455892.26 -0.2908522.27 -0.3332082.28 -0.3722362.29 -0.4075442.3 -0.43878

2.31 -0.4656312.32 -0.4878312.33 -0.5051562.34 -0.5174332.35 -0.5245412.36 -0.5264082.37 -0.5230152.38 -0.5143962.39 -0.5006372.4 -0.481877

2.41 -0.4583012.42 -0.4301472.43 -0.3976942.44 -0.3612682.45 -0.3212322.46 -0.2779872.47 -0.231964


63/74


64/74

2.93 -0.4436092.94 -0.4696962.95 -0.491092.96 -0.5075772.97 -0.5189932.98 -0.525223

2.99 -0.5262053 -0.521929


65/74

OK

Hasta que ϖ ω

1 1.5 2 2.5 3 3.5

X$(t)

X#( !


66/74


67/74


68/74


69/74


70/74


71/74


72/74


73/74

t Vs X%(t)

t Vs X$(t)

0 0.5 1 1.5 2 2.5 3 3.5

-0.08

-0.06

-0.04

-0.02

0

0.02

0.04

0.06

0.08

Co$%mn &Co$%mn &

0 0.5 1 1.5 2 2.5 3 3.5

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

Co$%mn '

Co$%mn '


74/74

Documents

Pregunta1.xlsx