PROBLEM SET NO.

3
1. The structural frame shown has a rigid beam and is rigid jointed at both ends of the
three columns. The mass of the structure of 6000 kg is concentrated at the top. The
columns are 3.2 m long and each has an EI = 4.6 x 10 6 N-m2. The structure has a viscous
damping (h) of 5%. Model the structure as an SDOF shear building. A blast load F(t) is
applied as shown.

a. Analyze using numerical integration by Newmark’s constant acceleration method

the response (displacement, velocity and acceleration) with respect to time in
intervals of 0.01 sec, if the mass (initially set at rest) moved to the due to a blast load
F(t) directed to the right as shown. Show spread sheet results. Summarize equations
used. Plot the responses, x(t), v(t), a(t) from t = 0s to t = 1.0s.

b. Determine the maximum displacement produced by the blast load and the resulting
shear force and bending moment in the columns.

2. If F(t) in Problem 1 is replaced by ground motion (ug), plot the acceleration data,
velocity data, and displacement data in time domain. Determine the maximum
acceleration, velocity and displacement. Use numerical integration by Newmark’s
constant acceleration method to complete the velocity and displacement data. Consider
the Taiwan ground motion data attached herewith.

Solution: ξ = 0.05

1. m = 6000 kg Stiffness, k:
EI = 4.6 x 106 N-m2
 12 EI 12( 4.6 x 106 ) 12
k = 3 x 3= x 3=5.054 x 10 6 N /m at t=0 ¿ 0.25: F ¿i= t
L 3.23 0.25

12
Natural frequency, ⍵: at t=0.26 ¿ 0.50: F ¿i= (0.5−t)
0.25

k 5.054 x 106 at t=0.51¿ 1.00 : F ¿i =0

ω n=
√ √ m
=
6,000
=29.023 rad / s
∆Fi = Fi+1 – Fi
Damping coefficient, c: ui+1 = ui + ∆ui

c = ξ x 2m⍵n ů i+1 = ů i + ∆ů i
c = 0.05 (2 x 6,000 x 29.023) = 17413.8
ü i+1 = ü i + ∆ü i
Newmark’s Constant Acceleration ∆F
method:
i∗¿=∆ F i + ( 4∆mt +2 c ) ů +2 m ü ¿
i i

F
∆t ∆ t2 ∆t ∆=∆t 2 i∗¿ ¿
( m+ c +
2 4 ) ( ∆ u
k üi +1=f i+1−c u̇ i+ üi −k ui +∆ t u̇i+
2
i
) (
ü
4 ki i∗¿ ¿ )
u̇i +1=u̇i +
∆t
(ü + ü )
2 i i +1
∆ ů i= ( ∆2t ) ∆ u −2u i i

∆t 2 4
ui +1=ui +∆ t u̇ i+ ( üi+ üi+1 ) ∆ ü i= ( ∆ ui−∆ t ůi )−2üi
4 ∆ t2

Initial conditions:

u0 = 0 m
ů 0 = 0 m/s
ü 0 = 0 N/m2
F0 = 0 N
Δt = 0.01 s

k 2c 4m 2 x17413.8 4 x 6,000
i∗¿=k + + =5.054 x 10 6+ + ¿
∆ t ∆ t2 0.01 ¿¿

Summary of computed values using Newmark’s Constant Acceleration method:

tί Fί ∆Fί uί ůί üί ∆F•ί ∆uί ∆ůί ∆üί
 1.9313E- 3.86261E- 7.72522E-
0.00 0 0.48 0 0 0 0.48
09 07 05
1.9313E- 3.86261E- 7.72522E- 9.4453E- 1.11654E- 6.88034E-
0.01 0.48 0.48 2.3475
09 07 05 09 06 05
1.13766E- 1.5028E- 0.0001460 2.37056E- 1.73553E- 5.49949E-
0.02 0.96 0.48 5.8917
08 06 56 08 06 05
3.50822E- 3.23833E- 0.0002010 4.33633E- 2.19601E- 3.71002E-
0.03 1.44 0.48 10.777
08 06 5 08 06 05
7.84456E- 5.43433E- 0.0002381 6.66681E- 2.46495E- 1.66892E-
0.04 1.92 0.48 16.569
08 06 51 08 06 05
1.45114E- 7.89929E- 0.0002548 9.16222E- 2.52586E- -4.5072E-
0.05 2.4 0.48 22.771
07 06 4 08 06 06
2.36736E- 1.04251E- 0.0002503 1.1615E- 2.37961E- -2.4743E-
0.06 2.88 0.48 28.867
07 05 33 07 06 05
3.52885E- 1.28048E- 0.0002255 1.38267E- 2.0439E- -4.2399E-
0.07 3.36 0.48 34.364
07 05 9 07 06 05
4.91152E- 1.48487E- 0.0001831 1.56243E- 1.55135E- -5.6111E-
0.08 3.84 0.48 38.832
07 05 91 07 06 05
6.47396E- 0.0001270 1.68732E- 9.46414E- -6.4876E-
0.09 4.32 0.48 1.64E-05 41.936
07 79 07 07 05
8.16128E- 1.73464E- 6.22036E- 1.74871E- 2.81452E- -6.8117E-
0.10 4.8 0.48 43.462
07 05 05 07 07 05
1.76279E- -5.9133E- 1.7434E- -3.8777E- -6.5727E-
0.11 5.28 0.48 9.91E-07 43.33
05 06 07 07 05
1.16534E- 1.72401E- 1.67368E- -1.0067E- -5.8058E-
0.12 5.76 0.48 -7.164E-05 41.597
06 05 07 06 05
1.33271E- 1.62334E- - 1.54702E- -1.5264E- -4.5881E-
0.13 6.24 0.48 38.449
06 05 0.0001297 07 06 05
-
1.48741E- 1.4707E- 1.37534E- -1.9074E- -3.0313E-
0.14 6.72 0.48 0.0001755 34.182
06 05 07 06 05
8
-
1.62494E- 1.27997E- 1.17384E- -2.1225E- -1.2717E-
0.15 7.2 0.48 0.0002058 29.174
06 05 07 06 05
9
-
1.74233E- 1.06772E- 9.59769E- 5.42148E-
0.16 7.68 0.48 0.0002186 23.854 -2.159E-06
06 05 08 06
1
-
1.8383E- 8.5182E- 7.50879E- -2.0188E- 2.26102E-
0.17 8.16 0.48 0.0002131 18.662
06 06 08 06 05
9
-
1.91339E- 6.49938E- 5.64019E- -1.7184E- 3.74781E-
0.18 8.64 0.48 0.0001905 14.018
06 06 08 06 05
8
1.96979E- - 4.13771E- -1.2866E- 4.88808E-
0.19 9.12 0.48 4.781E-06 10.284
06 0.0001531 08 06 05
-
2.01117E- 3.49441E- 3.11329E- -7.6224E- 5.5988E-
0.20 9.6 0.48 0.0001042 7.7377
06 06 08 07 05
2
2.0423E- 2.73217E- 2.63688E- -1.9059E- 5.83419E-
0.21 10.08 0.48 -4.823E-05 6.5536
06 06 08 07 05
2.06867E- 2.54158E- 1.01117E- 2.73185E- 3.80538E- 5.58843E-
0.22 10.56 0.48 6.7896
06 06 05 08 07 05
2.09599E- 2.92212E- 6.5996E- 3.37447E- 9.0471E-
0.23 11.04 0.48 8.3868 4.895E-05
06 06 05 08 07
0.24 11.52 0.48 2.12974E- 3.82683E- 0.0001149 11.177 4.49713E- 1.3406E- 3.82284E-
 06 06 46 08 06 05
-
2.17471E- 5.16743E- 0.0001531 5.60878E- 8.8271E-
0.25 12 -0.48 13.94 0.0001298
06 06 74 08 07
1
-
2.23079E- 6.05014E- 2.33678E- 5.8468E- -4.0667E-
0.26 11.52 -0.48 14.531 0.0001280
06 06 05 08 07
7
-
2.28926E- 5.64347E- - 4.83005E- -1.6268E-
0.27 11.04 -0.48 12.004 0.0001159
06 06 0.0001047 08 06
6
-
2.33756E- 4.01664E- 2.6764E- -2.6805E- -9.4765E-
0.28 10.56 -0.48 0.0002206 6.6518
06 06 08 06 05
7
-
2.36433E- 1.33616E- -4.0712E- -3.4866E- -6.6452E-
0.29 10.08 -0.48 0.0003154 -1.0118
06 06 09 06 05
3
-
2.36026E- -2.1504E- -4.1436E- -3.9865E- -3.3527E-
0.30 9.6 -0.48 0.0003818 -10.298
06 06 08 06 05
8
-
2.31882E- -6.1368E- -8.2109E- -4.1481E- 1.20196E-
0.31 9.12 -0.48 0.0004154 -20.407
06 06 08 06 06
1
-
2.23671E- -1.0285E- -1.2269E- -3.9678E- 3.48599E-
0.32 8.64 -0.48 0.0004142 -30.492
06 05 07 06 05
1
-
2.11402E- -1.4253E- -1.5988E- -3.4698E- 6.4739E-
0.33 8.16 -0.48 0.0003793 -39.735
06 05 07 06 05
5
-
1.95415E- -1.7722E- -1.9074E- -2.7035E- 8.85148E-
0.34 7.68 -0.48 0.0003146 -47.406
06 05 07 06 05
1
-
1.76341E- -2.0426E- -2.1295E- -1.7388E- 0.0001044
0.35 7.2 -0.48 0.0002260 -52.927
06 05 07 06 24
9
-
1.55045E- -2.2165E- -2.2495E- -6.5971E- 0.0001113
0.36 6.72 -0.48 0.0001216 -55.907
06 05 07 07 94
7
1.32551E- -2.2824E- -1.0274E- -2.2603E- 4.42801E- 0.0001091
0.37 6.24 -0.48 -56.177
06 05 05 07 07 08
1.09947E- -2.2382E- 9.88341E- -2.1642E- 1.4784E- 9.80111E-
0.38 5.76 -0.48 -53.79
06 05 05 07 06 05
8.8305E- -2.0903E- 0.0001968 -1.9721E- 2.36472E- 7.92528E-
0.39 5.28 -0.48 -49.014
07 05 45 07 06 05
6.85841E- -1.8539E- 0.0002760 -1.7022E- 3.03385E- 5.45738E-
0.40 4.8 -0.48 -42.305
07 05 98 07 06 05
5.15624E- -1.5505E- 0.0003306 -1.3786E- 3.43746E- 2.61475E-
0.41 4.32 -0.48 -34.263
07 05 72 07 06 05
3.77764E- -1.2067E- 0.0003568 -1.0292E- 3.55015E- -3.6091E-
0.42 3.84 -0.48 -25.58
07 05 19 07 06 06
2.74842E- -8.5171E- 0.0003532 -6.8317E- 3.37091E- -3.2238E-
0.43 3.36 -0.48 -16.979
07 06 1 08 06 05
2.06526E- -5.1462E- 0.0003209 -3.6849E- 2.92251E- -5.7442E-
0.44 2.88 -0.48 -9.1584
07 06 72 08 06 05
1.69676E- -2.2237E- 0.0002635 -1.0992E- 2.24896E- -7.7268E-
0.45 2.4 -0.48 -2.732
07 06 3 08 06 05
 1.58684E- 2.52644E- 0.0001862 7.3094E- 1.41135E- -9.0253E-
0.46 1.92 -0.48 1.8167
07 08 62 09 06 05
1.65994E- 1.43662E- 9.60085E- 1.67783E- 4.8242E- -9.5533E-
0.47 1.44 -0.48 4.17
07 06 05 08 07 05
1.82772E- 1.91904E- 4.75508E- 1.68918E- -4.5972E- -9.2894E-
0.48 0.96 -0.48 4.1982
07 06 07 08 07 05
1.99664E- 1.45932E- -9.2419E- 7.90292E- -1.3381E- -8.2773E-
0.49 0.48 -0.48 1.9642
07 06 05 09 06 05
-
2.07567E- 1.21264E- -7.2708E- -1.6967E- 1.10487E-
0.50 0 0 0.0001751 -1.807
07 07 09 06 05
9
-
2.00296E- -1.5754E- -2.3359E- 2.40905E-
0.51 0 0 0.0001641 -5.8056 -1.521E-06
07 06 08 05
4
-
1.76937E- -3.0964E- -3.7096E- -1.2265E- 3.48072E-
0.52 0 0 0.0001400 -9.2198
07 06 08 06 05
5
-
1.3984E- -4.3229E- -4.7431E- 4.23924E-
0.53 0 0 0.0001052 -11.788 -8.405E-07
07 06 08 05
5
9.24089E- -5.1634E- -6.2853E- -5.3619E- -3.9695E- 4.63168E-
0.54 0 0 -13.326
08 06 05 08 07 05
3.87903E- -5.5603E- -1.6537E- -5.5271E- 6.64533E- 4.63638E-
0.55 0 0 -13.737
08 06 05 08 08 05
-1.6481E- -5.4939E- 2.98273E- -5.2382E- 5.11464E- 4.26383E-
0.56 0 0 -13.019
08 06 05 08 07 05
-6.8862E- -4.9824E- 7.24655E- -4.5312E- 3.5549E-
0.57 0 0 -11.262 9.024E-07
08 06 05 08 05
-1.1417E- 0.0001080 -3.4755E- 1.20898E- 2.57667E-
0.58 0 0 -4.08E-06 -8.638
07 14 08 06 05
-1.4893E- 0.0001337 -2.1667E- 1.40863E- 1.41628E-
0.59 0 0 -2.871E-06 -5.3851
07 81 08 06 05
-1.4624E- 0.0001479 -7.1837E- 1.4881E- 1.73212E-
0.60 0 0 -1.706E-07 -1.7854
06 44 09 06 06
-1.7778E- 2.56852E- 0.0001496 7.47838E- 1.44431E- -1.0491E-
0.61 0 0 1.8587
07 08 76 09 06 05
1.46999E- 0.0001391 2.11212E- 1.28426E- -2.1518E-
0.62 0 0 -1.703E-07 5.2494
06 85 08 06 05
-1.4918E- 2.75425E- 0.0001176 3.26637E- 1.02424E- -3.0486E-
0.63 0 0 8.1181
07 06 67 08 06 05
-1.1652E- 3.77849E- 8.71803E- 4.12258E- 6.88187E- -3.6723E-
0.64 0 0 10.246
07 06 05 08 07 05
-7.5292E- 4.46667E- 5.04572E- 4.61946E- 3.05581E- -3.9798E-
0.65 0 0 11.481
08 06 05 08 07 05
-2.9097E- 4.77225E- 1.0659E- 4.72667E- -9.1159E-
0.66 0 0 11.748 -3.955E-05
08 06 05 08 08
1.81696E- 4.68109E- -2.8891E- 4.44641E- -4.6936E- -3.6091E-
0.67 0 0 11.051
08 06 05 08 07 05
6.26337E- 4.21173E- -6.4982E- 3.81233E- -7.9879E- -2.9794E-
0.68 0 0 9.475
08 06 05 08 07 05
1.00757E- 3.41294E- -9.4776E- 2.88593E-
0.69 0 0 7.1726 -1.054E-06 -2.125E-05
07 06 05 08
-
1.29616E- 2.35892E- 1.75075E- -1.2163E- -1.1217E-
0.70 0 0 0.0001160 4.3513
07 06 08 06 05
3
 -
1.47124E- 1.14257E- 5.04975E- -1.2752E- -5.5257E-
0.71 0 0 0.0001272 1.255
07 06 09 06 07
4
1.52174E- -1.3262E- - -7.4696E- -1.2287E- 9.85785E-
0.72 0 0 -1.8565
07 07 0.0001278 09 06 06
-
1.44704E- -1.3613E- -1.0835E- 1.91747E-
0.73 0 0 0.0001179 -4.7298 -1.903E-08
07 06 06 05
4
1.25674E- -2.4448E- -9.8763E- -2.8719E- -8.5428E- 2.66707E-
0.74 0 0 -7.1378
07 06 05 08 07 05
9.69541E- -3.2991E- -7.2093E- -3.5801E- -5.6199E- 3.17873E-
0.75 0 0 -8.8978
08 06 05 08 07 05
6.11533E- -3.8611E- -4.0305E- -3.9772E- -2.3218E- 3.41748E-
0.76 0 0 -9.8847
08 06 05 08 07 05
2.13817E- -4.0933E- -6.1306E- -4.0396E- 1.07272E- 3.37157E-
0.77 0 0 -10.04
08 06 06 08 07 05
-1.9015E- 2.75851E- -3.7717E- 4.28486E- 3.0527E-
0.78 0 0 -3.986E-06 -9.3742
08 05 08 07 05
-5.6732E- -3.5575E- 5.81121E- -3.2046E- 7.05844E- 2.49446E-
0.79 0 0 -7.9645
08 06 05 08 07 05
-8.8778E- -2.8517E- 8.30567E- -2.3926E- 9.18016E- 1.74897E-
0.80 0 0 -5.9466
08 06 05 08 07 05
-1.9336E- 0.0001005 -1.4089E- 1.04957E- 8.82106E-
0.81 0 0 -1.127E-07 -3.5015
06 46 08 06 06
-1.2679E- -8.8407E- 0.0001093 -3.3804E- 1.09206E- -3.2211E-
0.82 0 0 -0.8401
07 07 67 09 06 07
-1.3017E- 2.07997E- 0.0001090 7.30266E- 1.04454E- -9.1828E-
0.83 0 0 1.815
07 07 45 09 06 06
-1.2287E- 1.25254E- 9.98625E- 1.70923E- 9.13384E- -1.7048E-
0.84 0 0 4.2481
07 06 05 08 07 05
-1.0578E- 2.16592E- 8.28142E- 2.52172E- 7.11609E- -2.3307E-
0.85 0 0 6.2674
07 06 05 08 07 05
-8.0561E- 2.87753E- 5.95076E- 3.10633E- 4.57607E- -2.7494E-
0.86 0 0 7.7204
08 06 05 08 07 05
-4.9497E- 3.33514E- 3.20138E- 3.42189E- 1.73502E- -2.9327E-
0.87 0 0 8.5046
08 06 05 08 07 05
-1.5279E- 3.50864E- 2.68655E- 3.45026E- -1.1675E- -2.8724E-
0.88 0 0 8.5752
08 06 06 08 07 05
1.9224E- 3.39188E- -2.6037E- 3.19719E- -3.8938E- -2.5801E-
0.89 0 0 7.9462
08 06 05 08 07 05
5.1196E- 3.00251E- -5.1838E- 2.69116E- -6.2269E- -2.0861E-
0.90 0 0 6.6885
08 06 05 08 07 05
7.81076E- 2.37982E- 1.98041E- -7.9881E- -1.4363E-
0.91 0 0 -7.27E-05 4.922
08 06 08 07 05
9.79117E- -8.7063E- 1.12849E- -9.0502E-
0.92 0 0 1.581E-06 2.8047 -6.879E-06
08 05 08 07
1.09197E- 6.75982E- -9.3942E- 2.0866E- -9.3464E- 9.55003E-
0.93 0 0 0.5186
07 07 05 09 07 07
1.11283E- -2.5866E- -9.2987E- -7.0237E- -8.8741E- 8.4918E-
0.94 0 0 -1.7456
07 07 05 09 07 06
1.0426E- -1.1461E- -8.4495E- -1.5307E- -7.6932E- 1.51266E-
0.95 0 0 -3.8044
07 06 05 08 07 05
8.89522E- -1.9154E- -6.9368E- -2.2114E- -5.9196E- 2.03451E-
0.96 0 0 -5.4961
08 06 05 08 07 05
0.97 0 0 6.68386E- -2.5073E- -4.9023E- -6.6932 -2.6931E- -3.7142E- 2.37625E-
 08 06 05 08 07 05
3.9908E- -2.8788E- -2.5261E- -2.9422E- -1.2685E- 2.51512E-
0.98 0 0 -7.3124
08 06 05 08 07 05
1.04861E- -3.0056E- -1.0955E- 1.21181E- 2.44553E-
0.99 0 0 -7.3195 -2.945E-08
08 06 07 07 05
-1.8964E- -2.8844E- 2.43457E- -2.7082E- 3.52405E- 2.17896E-
1.00 0 0 -6.731
08 06 05 08 07 05

Displacement (m)
0

0
0.01 0.05 0.09 0.13 0.17 0.21 0.25 0.29 0.33 0.37 0.41 0.45 0.49 0.53 0.57 0.61 0.65 0.69 0.73 0.77 0.81 0.85 0.89 0.93 0.97 1.01
0

Time (s)

Velocity (m/s)
0

0
0.01 0.05 0.09 0.13 0.17 0.21 0.25 0.29 0.33 0.37 0.41 0.45 0.49 0.53 0.57 0.61 0.65 0.69 0.73 0.77 0.81 0.85 0.89 0.93 0.97 1.01
0

Time (s)
 Acceleration (m/s2)
0

0
0.01 0.05 0.09 0.13 0.17 0.21 0.25 0.29 0.33 0.37 0.41 0.45 0.49 0.53 0.57 0.61 0.65 0.69 0.73 0.77 0.81 0.85 0.89 0.93 0.97 1.01
0

Time (s)

b. Maximum displacement from the graph, δmax:

δmax = 2.36433 x 10-6 m

Resulting shear force, F:

F = k δmax
F = (5.054 x 106)(2.36433 x 10-6)
F = 11.95 N

Bending moment in the columns:

M = FL
M = (11.95)(3.2)
M = 38.24 N-m
2. If F(t) in Problem 1 is replaced by ground motion (ug), plot the acceleration data,
velocity data, and displacement data in time domain. Determine the maximum
acceleration, velocity and displacement. Use numerical integration by Newmark’s
constant acceleration method to complete the velocity and displacement data. Consider
the Taiwan ground motion data attached herewith.

TIME HISTORY DATA

0.20000000
0.15000000
0.10000000
0.05000000
0.00000000
-0.05000000
-0.10000000
-0.15000000
-0.20000000
0 5 10 15 20 25 30 35 40

m = 6000 kg
EI = 4.6 x 106 N-m2 Newmark’s Constant Acceleration
ξ = 0.05 method:
k = 5.054 x 106 N/m ∆t ∆ t2 ∆t ∆ t2
⍵ = 29.023 rad/s
c = 17413.8
(m+ c +
2 4 ) ( 2 ) (
k üi +1=f i+1−c u̇ i+ üi −k ui +∆ t u̇i+
4
u
[6000 + (0.005 x 17413.8) + (0.000025)(5.054 x
106)] ü i+1 = -94.5213 – 17413.8 [0 + 0.005(0)] –
(5.054 x 106) (0 + 0.001(0) + 0.000025(0)]
Initial conditions:
ü i+1 = -0.015212445 m/s2 u0 = 0 m
ů 0 = 0 m/s
∆t ü 0 = 0 N/m2
u̇i +1=u̇i + (ü + ü ) Δt = 0.01 s
2 i i +1

ů i+1 = 0 + 0.005(0-0.015212445) Fi+1 = -m x ü g x g

Fi+1 = -6000(0.00160587)(9.81)
ů i+1 = -7.6062225x10-5 m/s
Fi+1 = -94.52 N

ui+1 = ui + ∆ui
∆t
2 ů i+1 = ů i + ∆ů i
ui +1=ui +∆ t u̇ i+ ( üi+ üi+1 ) ü i+1 = ü i + ∆ü i
4
F i∗¿
∆ u i=∆ ¿
ui+1 = 0 + 0.01(0) + (0.000025)(0- k i∗¿ ¿
0.015212445) 2
-7
( )
∆ ů i=
∆t
∆ ui−2ui
ui+1 = -3.80311125x10 m 4
∆ ü i= 2 ( ∆ ui−∆ t ůi )−2üi
∆t

Summary of computed values using Newmark’s Constant Acceleration method:

tί üg m x üg x g uί ůί üί
0.00 0.00413052 243.1224072 0 0 0
0.01 0.00160587 94.5215082 -3.81E-07 -7.61E-05 -0.01522154
-
0.00149949 -1.84E-06 -0.01257915
0.02 88.2599814 0.000215111
-
0.0005037 -4.32E-06 -0.00057811
0.03 29.647782 0.000280897
-
-0.00220545 -6.46E-06 0.02737649
0.04 -129.812787 0.000146905
0.02724096
-0.00226284 -6.56E-06 0.000126182
0.05 -133.1907624 9
0.01459649
-0.00122895 -4.25E-06 0.000335369
0.06 -72.335997 5
0.07 0.00164611 96.8900346 -9.41E-07 0.000326796 -0.01631122
0.08 0.00449629 264.6516294 7.99E-07 2.11E-05 -0.04482729
-
0.00554503 -1.41E-06 -0.05190829
0.09 326.3804658 0.000462575
-
0.00555751 -8.45E-06 -0.04483772
0.10 327.1150386 0.000946305
 -
0.00454784 -1.97E-05 -0.02470494
0.11 267.6858624 0.001294018
-
0.00181789 -3.29E-05 0.01314235
0.12 107.0010054 0.001351831
- 0.02395369
0.0017191 -4.55E-05
0.13 101.186226 0.001166351 8
- 0.03155532
0.0017261 -5.58E-05
0.14 101.598246 0.000888806 1
- 0.03633352
0.00174368 -6.29E-05
0.15 102.6330048 0.000549362 5
-
0.00176171 -6.66E-05 0.03808229
0.16 103.6942506 0.000177282
0.03675064
0.00177974 -6.65E-05 0.000196882
0.17 104.7554964 9
0.18 0.00178521 105.0774606 -6.28E-05 0.000543881 0.03264908
0.02618383
0.00177782 -5.59E-05 0.000838045
0.19 104.6424852 7
0.01793786
0.00175728 -4.64E-05 0.001058654
0.20 103.4335008 8
0.00855632
0.00173001 -3.51E-05 0.001191125
0.21 101.8283886 6
0.22 0.00169478 99.7547508 -2.30E-05 0.001228053 -0.00117076
0.23 0.00158536 93.3142896 -1.10E-05 0.001173041 -0.0098316
0.24 0.00064057 37.7039502 2.16E-07 0.001076126 -0.00955134
0.25 -0.00037119 -21.8482434 1.05E-05 0.000988952 -0.00788359
0.00223632
-0.00221332 2.03E-05 0.000960715
0.26 -130.2760152 3
0.27 -0.00228875 -134.715825 2.98E-05 0.000947655 -0.00484846
0.28 -0.00229308 -134.9706888 3.89E-05 0.000863289 -0.01202465
0.29 -0.00221927 -130.6262322 4.67E-05 0.00070924 -0.01878511
0.30 -0.00218191 -128.4272226 5.28E-05 0.00049773 -0.02351701
0.31 -0.00204203 -120.1938858 5.65E-05 0.000244059 -0.02721716
-
0.00069358 5.69E-05 -0.053252
0.32 40.8241188 0.000158287
-
0.00083051 5.28E-05 -0.04969289
0.33 48.8838186 0.000673011
-
0.00079674 4.38E-05 -0.04065823
0.34 46.8961164 0.001124767
-
-0.0010453 3.12E-05 -0.0114971
0.35 -61.526358 0.001385544
0.01870189
-0.00298559 1.75E-05 -0.00134952
0.36 -175.7318274 7
-
-0.0057354 5.88E-06 0.05424745
0.37 -337.585644 0.000984773
0.38 -0.00585696 -344.7406656 -1.12E-06 - 0.05957592
 0.000415656 5
0.06710958
-0.00672716 -2.11E-06 0.000217771
0.39 -395.9606376 5
0.40 -0.00594191 -349.7408226 3.08E-06 0.000820319 0.05339992
0.04388228
-0.00600733 1.37E-05 0.00130673
0.41 -353.5914438 7
0.01482292
-0.00435184 2.82E-05 0.001600256
0.42 -256.1493024 2
0.43 -0.0035107 -206.639802 4.44E-05 0.001639913 -0.00689159
0.44 -0.00443973 -261.3225078 6.04E-05 0.001552074 -0.01067622
0.45 -0.00445348 -262.1318328 7.51E-05 0.001387785 -0.02218161
0.46 -0.00355272 -209.1130992 8.74E-05 0.001075525 -0.04027024
0.47 -0.00250799 -147.6202914 9.58E-05 0.000594096 -0.05601572
-
0.00026668 9.82E-05 -0.08326245
0.48 15.6967848 0.000102295
-
0.00139109 9.29E-05 -0.08748217
0.49 81.8795574 0.000956018
-
0.00413044 7.87E-05 -0.09992754
0.50 243.1176984 0.001893067
-
0.0041678 5.53E-05 -0.07846065
0.51 245.316708 0.002785008
-
0.00150489 2.48E-05 -0.02574744
0.52 88.5778254 0.003306048
- 0.00288477
0.00144453 -8.78E-06
0.53 85.0250358 0.003420362 2
- 0.02988321
0.00144852 -4.22E-05
0.54 85.2598872 0.003256522 2
-
0.00043981 -7.24E-05 0.06335285
0.55 25.8872166 0.002790341
-
-0.00316496 -9.58E-05 0.11545761
0.56 -186.2895456 0.001896289
- - 0.12413242
-0.00331012
0.57 -194.8336632 0.000108809 0.000698339 8
- 0.12100741
-0.00327841 0.00052736
0.58 -192.9672126 0.000109664 9
0.09946737
-0.00231116 -9.89E-05 0.001629734
0.59 -136.0348776 1
0.06217944
-0.00045495 -7.85E-05 0.002437968
0.60 -26.778357 3
0.02924164
0.00052917 -5.19E-05 0.002895074
0.61 31.1469462 4
0.62 0.00144204 84.8784744 -2.23E-05 0.003019106 -0.00443526
0.63 0.00145207 85.4688402 7.07E-06 0.002855593 -0.02826727
0.64 0.00141314 83.1774204 3.37E-05 0.002470638 -0.04872375
0.65 0.0013849 81.515214 5.56E-05 0.001902844 -0.06483509
0.66 0.0013447 79.149042 7.11E-05 0.001202546 -0.07522437
0.67 0.00134135 78.951861 7.92E-05 0.000427996 -0.07968576
-
0.00133968 7.96E-05 -0.07769523
0.68 78.8535648 0.000358909
-
0.00138184 7.23E-05 -0.06998957
0.69 81.3351024 0.001097333
-
0.00141334 5.82E-05 -0.05682449
0.70 83.1891924 0.001731404
-
0.00146303 3.84E-05 -0.0396729
0.71 86.1139458 0.002213891
-
0.00150743 1.48E-05 -0.01978824
0.72 88.7273298 0.002511196
- 0.00147902
0.00151398 -1.08E-05
0.73 89.1128628 0.002602742 2
- 0.02211301
0.00151269 -3.62E-05
0.74 89.0369334 0.002484782 9
- 0.04041582
0.00151123 -5.95E-05
0.75 88.9509978 0.002172138 7
- 0.05481671
0.0015284 -7.88E-05
0.76 89.961624 0.001695975 2
- 0.06463863
0.00152609 -9.28E-05
0.77 89.8256574 0.001098699 4
-
0.00146498 -0.00010042 0.06959923
0.78 86.2287228 0.000427509
0.07818965
0.00042183 -0.000101 0.000311435
0.79 24.8289138 5
0.09825357
-0.00251366 -9.35E-05 0.001193651
0.80 -147.9540276 9
0.11763424
-0.00626103 -7.61E-05 0.00227309
0.81 -368.5242258 6
0.07654955
-0.00467409 -4.86E-05 0.003244009
0.82 -275.1169374 6
0.04590855
-0.0047117 -1.31E-05 0.0038563
0.83 -277.330662 8
0.00392943
-0.00384908 2.68E-05 0.00410549
0.84 -226.5568488 2
0.85 -0.00293128 -172.5351408 6.70E-05 0.003936531 -0.03772131
0.86 -0.00016559 -9.7466274 0.000103069 0.003284278 -0.09272924
0.87 0.00080019 47.0991834 0.000130549 0.002211791 -0.12176812
0.88 0.0008375 49.29525 0.000146335 0.000945419 -0.13150632
-
0.0008564 0.000149244 -0.13033001
0.89 50.407704 0.000363763
-
0.00089296 0.000139373 -0.11897766
0.90 52.5596256 0.001610301
0.91 0.00107811 63.4575546 0.000117799 -0.00270457 -0.0998761
 -
0.0047958 8.56E-05 -0.10683668
0.92 282.280788 0.003738134
0.93 0.00682995 402.010857 4.33E-05 -0.00471802 -0.08914062
-
0.00783108 -7.48E-06 -0.0550468
0.94 460.9373688 0.005438957
-
0.00779745 -6.34E-05 -0.00770791
0.95 458.957907 0.005752731
- - 0.06449895
0.00506648
0.96 298.2130128 0.000119546 0.005468776 8
- - 0.11430725
0.00394553
0.97 232.2338958 0.000169764 0.004574745 3
- - 0.16890935
0.00121298
0.98 71.3960028 0.000208431 0.003158662 2
- - 0.19181597
0.0002458
0.99 14.467788 0.000230999 0.001355035 2
- 0.18953817
0.00025741 0.000551736
1.00 15.1511526 0.000235016 5

DISPLACEMENT (m)
0.01
0
0
0
0
0
0
0
0
0
-0.01
0 5 10 15 20 25 30 35 40

Maximum displacement = 0.004437571 m

 VELOCITY (m/s)
0.15

0.1

0.05

-0.05

-0.1
0 5 10 15 20 25 30 35 40

Maximum velocity = 0.094538121 m/s

ACCELERATION (m/s2)
2.5
2
1.5
1
0.5
0
-0.5
-1
-1.5
-2
-2.5
0 5 10 15 20 25 30 35 40

Maximum acceleration = 2.26085369 m/s2