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Question: the motion xlt of a single degree of freedom system...

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The motion xlt) of a single degree of freedom system as shown in the Figure is governed by the equation where the external excitation force F(t) is positive in the positive x(t) direction If the external excitation is a harmonic force such as the motion x() becomes x(t)X sin(st-).where the amplitude of the response is and the phase angle is if the external excitation F(C) is an impulse denoted by F, the response of the single degree of freedom system is x() Fh(t) where h(t) is the unit impulse response function of the system is given by mod Here, a,-ω11-7 is the damped frequency of the free motion and ratio. ζ--is the damping 2mia Assignment: Show that the response x(0) X sin(at-0) of the system to the harmonic excitation FO) Fosinot can be calculated by the discrete Convolution Integra which represents the sum of all contributions by the impulses 12.3. N) to the response for all t 2 ξί System m - 2 kg k-75 N/m Excitation:Fo 1N5.75 rad/s 6.1237 rad/s 仁0.5, 0. 3, 0.1.0.05. 0. 01
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