# hw10 - ME 365 HOMEWORK 10 Out: November 10, 2011 Due:...

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HOMEWORK 10 Fall 2011 Out: November 10, 2011 Due: November 17, 2011 Problem 1 A wheel is rolling with linear velocity V over an infinite set of speed bumps as shown in the figure below. The bumps are H x W in size and spaced D apart. As the wheel rolls over a bump, the vertical position of the wheel hub rises then falls. The hub’s position, x(t), follows a sinusoid during this motion, as shown in the bottom portion of the figure. The wheel’s vertical displacement x(t) is given by, x ( t ) = 0 for T 2 < t < δ 2 T = D V H cos π t for 2 < t < + 2 where 0 for + 2 < t < + T 2 = W V (a) Show through simulation that the Fourier coefficients and fundamental frequency for the periodic signal x(t) are ω 1 = 2 V D A o 2 = 2 HW D A k = HW D sinc kW D + 1 2 + sinc kW D 1 2 B k = 0 where sinc ( a ) = ) a and sinc (0) = 1 (note there is a sinc function built into Matlab.)

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## This note was uploaded on 12/26/2011 for the course ME 365 taught by Professor Merkle during the Fall '07 term at Purdue University-West Lafayette.

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hw10 - ME 365 HOMEWORK 10 Out: November 10, 2011 Due:...

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