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In Section 5.2 we developed recurrence formulas for numerical solution of the equation of motion of a linear SDF system based on linear interpolation of the forcing function p(t) over each time step. Develop a similar procedure using a piecewise-constant representation of the forcing function wherein the value of the force in the interval t_{i} to t_{i+1 }is a constant equal to (Fig. P5.1). Show that the recurrence formulas for the response of an undamped system are
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