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Engineering · Mechanical Engineering
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The motion x(t) of a single degree of freedom system as shown in the Figure is governed by the equation mx(t) + cx(t) +kx(t)F(t) where the external excitation force F(t) is positive in the positive x(t) direction. r(c) If the external excitation is a harmonic force such as F(t) Fosinot the motion x(t) becomes x(t)-X sin(at-0), where the amplitude of the response is and the phase angle is -1 = tan if the external excitation F(t) is an impulse denoted by F, the response of the single degree of freedom system is x(t) Fh(t) where h(t) is the unit impulse response function of the system is given by h(t)sinwt mud Here, 6.d-dunV1-(* is the damped frequency of the free motion and ζ ratio. is the damping Assignment: Show that the response x(t)-X sin(mt-ø) of the system to the harmonic excitation F(t) Fosinot can be calculated by the discrete Convolution Integral which represents the sum of all ontributions by the impulses Fi( 1.2.3, N) to the response for all t System: m-2kg Fo 5N k=75N/m con = 6.1237 rad/s Excitation: 3.5rad/s ζ-0. 5,0. 3. 0. 1, 0.05, 0.0 1

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