Assume multiple single degree of freedom systems with natural periods T ∈ [0.05, 2.00] seconds with in-crement of period dT = 0.05 seconds. Assume three cases of damping ratio: Case (A) ξ = 0%; Case (B)ξ = 2%; Case (C) ξ = 5%. The systems are initially at rest. Thus, the initial conditions are u(t = 0) = 0 anḋu(t = 0) = 0. The systems are subjected to the base acceleration that was provided in the ElCentro.txt file(i.e., first column). For the systems in Case (A), Case (B), and Case (C) and for each natural period computethe peak acceleration, peak velocity, and peak displacement responses to the given base excitation. Please,use the Newmark method for β = 1/4 (average acceleration) to compute the responses. Create threeplots with three lines in each plot. The first plot will have the peak accelerations in y-axis and the naturalperiod of the system in x-axis. The second plot will have the peak velocities in y-axis and the natural periodof the system in x-axis. The third plot will have the peak displacement in y-axis and the natural period ofthe system in x-axis. The first line in each plot will be related to Case (A); The second line will be relatedto Case (B); The third line will be related to Case (C). Please, provide comments with your observations.
Assume multiple single degree of freedom systems with natural periods T ∈ [0.05, 2.00] seconds with in-
crement of period dT = 0.05 seconds. Assume three cases of damping ratio: Case (A) ξ = 0%; Case (B)
ξ = 2%; Case (C) ξ = 5%. The systems are initially at rest. Thus, the initial conditions are u(t = 0) = 0 and
̇u(t = 0) = 0. The systems are subjected to the base acceleration that was provided in the ElCentro.txt file
(i.e., first column). For the systems in Case (A), Case (B), and Case (C) and for each natural period compute
the peak acceleration, peak velocity, and peak displacement responses to the given base excitation. Please,
use the Newmark method for β = 1/4 (average acceleration) to compute the responses. Create three
plots with three lines in each plot. The first plot will have the peak accelerations in y-axis and the natural
period of the system in x-axis. The second plot will have the peak velocities in y-axis and the natural period
of the system in x-axis. The third plot will have the peak displacement in y-axis and the natural period of
the system in x-axis. The first line in each plot will be related to Case (A); The second line will be related
to Case (B); The third line will be related to Case (C). Please, provide comments with your observations.
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