story building. For this case, the analysis is limited to horizontal motion of the structure. Using Newton's second law, force balances can be developed for this system as dt² m₁ d²x₂ =+ k ·x₁ + = (x2-x₁) m₁ m3 = 8000 kg m k3 = 1800 kN/m k₂ m₁ = 10,000 kg -(x3 - x2) m |k₂ = 2400 kN/m m2 = (x2 − x3 ) - dt² m₁ = 12,000 kg m k₁ = 3000 kN/m m3 dt² m2 d²x3_k3 · (x₁ − x 2 ) + -=- Simulate the dynamics of this structure from t = 0 to 20 s, given the initial condition that the velocity of the ground floor is dx1/dt = 1 m/s, and all other initial values of displacements and velocities are zero. Present your results as two time-series plots of (a) displacements and (b) velocities. And develop a three- dimensional phase-plane plot of the displacements (X1, X2, X3). Use following functions: import matplotlib.pyplot as plt from mpl_toolkits.mplot3d import Axes 3D

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7th Edition
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Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
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Chapter1: Introduction
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story building. For this case, the analysis is limited to horizontal motion of the structure. Using Newton's
second law, force balances can be developed for this system as
dt²
m₁
d²x₂
=+
k
·x₁ + = (x2-x₁)
m₁
m3 = 8000 kg
m
k3 = 1800 kN/m
k₂
m₁ = 10,000 kg
-(x3 - x2)
m
|k₂ = 2400 kN/m
m2
= (x2 − x3 )
-
dt²
m₁ = 12,000 kg
m
k₁ = 3000 kN/m
m3
dt² m2
d²x3_k3
· (x₁ − x 2 ) +
-=-
Simulate the dynamics of this structure from t = 0 to 20 s, given the initial condition that the velocity of
the ground floor is dx1/dt = 1 m/s, and all other initial values of displacements and velocities are zero.
Present your results as two time-series plots of (a) displacements and (b) velocities. And develop a three-
dimensional phase-plane plot of the displacements (X1, X2, X3). Use following functions:
import matplotlib.pyplot as plt
from mpl_toolkits.mplot3d import Axes 3D
Transcribed Image Text:story building. For this case, the analysis is limited to horizontal motion of the structure. Using Newton's second law, force balances can be developed for this system as dt² m₁ d²x₂ =+ k ·x₁ + = (x2-x₁) m₁ m3 = 8000 kg m k3 = 1800 kN/m k₂ m₁ = 10,000 kg -(x3 - x2) m |k₂ = 2400 kN/m m2 = (x2 − x3 ) - dt² m₁ = 12,000 kg m k₁ = 3000 kN/m m3 dt² m2 d²x3_k3 · (x₁ − x 2 ) + -=- Simulate the dynamics of this structure from t = 0 to 20 s, given the initial condition that the velocity of the ground floor is dx1/dt = 1 m/s, and all other initial values of displacements and velocities are zero. Present your results as two time-series plots of (a) displacements and (b) velocities. And develop a three- dimensional phase-plane plot of the displacements (X1, X2, X3). Use following functions: import matplotlib.pyplot as plt from mpl_toolkits.mplot3d import Axes 3D
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