The single degree of freedom (SDOF) system the acceleration at the base (excitation) and the acceleration at the roof (response) of the SDOF system was recorded with sampling rate 50 Hz (50 samples per second, or dt= 0.02 seconds). The file ElCentro.txt includes the two columns of acceleration data. The first column lists the acceleration at the base of the SDOF system. The second column lists the acceleration at the roof of the SDOF system. (a) Plot the time histories of the recorded accelerations at the base and at the roof of the SDOF system. (b) Compute the acceleration, velocity and displacement time histories of the roof of the SDOF system subjected to the recorded base acceleration using the Central Difference method. Plot the accel- eration, velocity and displacement time histories. Plot the restoring force, the damping force, and the inertia force time histories. Compare the recorded acceleration time history at the roof of the SDOF with the acceleration that you computed using the numerical method. (c) Compute the acceleration, velocity and displacement time histories of the roof of the SDOF system subjected to the recorded base acceleration using the Newmark method for β = 1/6 (linear acceleration). Plot the acceleration, velocity and displacement time histories. Plot the restoring force, the damping force, and the inertia force time histories. Compare the recorded acceleration time history at the roof of the SDOF with the acceleration that you computed using the numerical method. (d) Compute the acceleration, velocity and displacement time histories of the roof of the SDOF system subjected to the recorded base acceleration using the Newmark method for β = 1/4 (average acceleration). Plot the acceleration, velocity and displacement time histories. Plot the restoring force, the damping force, and the inertia force time histories. Compare the recorded acceleration time history at the roof of the SDOF with the acceleration that you computed using the numerical method
The single degree of freedom (SDOF) system the acceleration at the base (excitation) and the acceleration at the roof (response) of the SDOF system was recorded with sampling rate 50 Hz (50 samples per second, or dt= 0.02 seconds). The file ElCentro.txt includes the two columns of acceleration data. The first column lists the acceleration at the base of the SDOF system. The second column lists the acceleration at the roof of the SDOF system. (a) Plot the time histories of the recorded accelerations at the base and at the roof of the SDOF system. (b) Compute the acceleration, velocity and displacement time histories of the roof of the SDOF system subjected to the recorded base acceleration using the Central Difference method. Plot the accel- eration, velocity and displacement time histories. Plot the restoring force, the damping force, and the inertia force time histories. Compare the recorded acceleration time history at the roof of the SDOF with the acceleration that you computed using the numerical method. (c) Compute the acceleration, velocity and displacement time histories of the roof of the SDOF system subjected to the recorded base acceleration using the Newmark method for β = 1/6 (linear acceleration). Plot the acceleration, velocity and displacement time histories. Plot the restoring force, the damping force, and the inertia force time histories. Compare the recorded acceleration time history at the roof of the SDOF with the acceleration that you computed using the numerical method. (d) Compute the acceleration, velocity and displacement time histories of the roof of the SDOF system subjected to the recorded base acceleration using the Newmark method for β = 1/4 (average acceleration). Plot the acceleration, velocity and displacement time histories. Plot the restoring force, the damping force, and the inertia force time histories. Compare the recorded acceleration time history at the roof of the SDOF with the acceleration that you computed using the numerical method
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