72bba6d2-e8f4-4262-91d7-b26e1a3ca41a 48 4 5 decimal

&[DATE] &[TIME] - &[FILENAME]

W 978.8 kip * :

W W kip / : 978.8

g 32.2 ft sec 2^/ * : in sec 2^/ 19325 /

g g sec 2^in / * : 386.4

m W g / : 2.5331

k 100 kip in / * :

k k in kip / * : 100

ζ 10 % * : 110 /

ω.n k m / sqrt : 6.2831

T.n 2 π * ω.n / : 1

c 2 ζ * ω.n * m * : 3.1832

t.start 0 sec * :

t.start t.start sec / : 0

t.end 5 sec * :

t.end t.end sec / : 5

Δt 0.1 sec * :

Δt Δt sec / : 110 /

Given / Assumed Initial Conditions

p 0 sec * 0 kip * 0.1 sec * 50 kip * 0.2 sec * 86.6 kip * 0.3 sec * 100 kip * 0.4 sec * 86.6 kip * 0.5 sec * 50 kip * 0.6 sec * 0 kip * 72 mat :

i 1 p rows range p i 1 el p i 1 el sec / : p i 2 el p i 2 el kip / : 21 line for

p 00 0.1 50 0.2 86.6 0.3 100 0.4 86.6 0.5 50 0.6 072 mat

Given / Assumed Initial Conditions

u.0 0 in * :

v.0 0 in sec / * :

a.0 0 in sec 2^/ * :

u.0 u.0 in / : 0

v.0 v.0 sec in / * : 0

a.0 a.0 sec 2^in / * :

Values for special condition (acceleration / )

γ 12 / :

β 14 / :

1. Initial Calculations [Table 5.4.2]

a.1 1 β Δt 2^* / m * γ β Δt * / c * + : 1076.9137

a.2 1 β Δt * / m * γ β / 1 - (c * + : 104.5082

a.3 12 β * / 1 - (m * Δt γ 2 β * / 1 - (* c * + : 2.5331

k.c k a.1 + : 1176.9137

2. ITERATIVE CALCULATIONS [Table 5.4.2]

R t.end t.start - Δt / 1 + 10 matrix :

i 0 R rows 1 - (range t i Δt * : pi p i 1 + (2 el : pi 0 : try pj p i 2 + (2 el : pj 0 : try i 0 ≡ ui u.0 : vi v.0 : ai a.0 : 13 mat ui R i (8 el : vi R i (9 el : ai R i (10 el : 13 mat if pcj pj a.1 ui * + a.2 vi * + a.3 ai * + : uj pcj k.c / : vj γ β Δt * / uj ui - (* 1 γ β / - (vi * + Δt 1 γ 2 β * / - (* ai * + : aj 1 β Δt 2^* / uj ui - (* 1 β Δt * / vi * - 12 β * / 1 - (ai * - : E i t pi ui vi ai pcj uj vj aj 110 mat : j 1 E cols range R i 1 + (j el E 1 j el : for 101 line for

ui u.0 : vi v.0 : ai a.0 : 13 mat

ui R i (8 el : vi R i (9 el : ai R i (10 el : 13 mat

0,0 axis system x y XY x y / - :

data R.t R stack :

R.t i t(i) p(i) u(i) v(i) a(i) pc(i+1) u(i+1 v(i+1) a(i+1) 110 mat :

R 00000050 0.0425 0.8497 16.9936 1 0.1 50 0.0425 0.8497 16.9936 264.1971 0.2245 2.7903 21.8188 2 0.2 86.6 0.2245 2.7903 21.8188 688.6277 0.5851 4.4223 10.8213 3 0.3 100 0.5851 4.4223 10.8213 1206.2953 1.025 4.3747 11.7728 - 4 0.4 86.6 1.025 4.3747 11.7728 - 1581.1722 1.3435 1.9958 35.8063 - 5 0.5 50 1.3435 1.9958 35.8063 - 1564.6963 1.3295 2.2758 - 49.6244 - 6 0.6 0 1.3295 2.2758 - 49.6244 - 1068.2064 0.9076 6.1614 - 28.0881 - 7 0.7 0 0.9076 6.1614 - 28.0881 - 262.3767 0.2229 7.5326 - 0.6647 8 0.8 0 0.2229 7.5326 - 0.6647 545.4475 - 0.4635 - 6.1953 - 26.0809 9 0.9 0 0.4635 - 6.1953 - 26.0809 1080.4935 - 0.9181 - 2.8971 - 39.8832 1010 0.9181 - 2.8971 - 39.8832 1190.4252 - 1.0115 - 1.0289 38.6371 1110 mat

xt R 2 col :

yu R 4 col :

yv R 5 col :

ya R 6 col :

xt yu augment XY 2 1 sys xt yv augment XY 2 1 sys xt ya augment 0 2 1 sys

G xt ya augment 1.0 * :

# # G XY 2 1 sys

Exponential threshold 15 G 11 el 1012 -^: G 12 el 1012 -^: 12 mat

G 00 0.1 16.9936 0.2 21.8188 0.3 10.8213 0.4 11.7728 - 0.5 35.8063 - 0.6 49.6244 - 72 mat

data i t(i) p(i) u(i) v(i) a(i) pc(i+1) u(i+1 v(i+1) a(i+1) 00000050 0.04 0.85 16.99 1 0.1 50 0.04 0.85 16.99 264.2 0.22 2.79 21.82 2 0.2 86.6 0.22 2.79 21.82 688.63 0.59 4.42 10.82 3 0.3 100 0.59 4.42 10.82 1206.3 1.02 4.37 11.77 - 4 0.4 86.6 1.02 4.37 11.77 - 1581.17 1.34 2 35.81 - 610 mat