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Unformatted text preview: ME163 Mechanical Vibrations (Winter 2009) HW-3 Due 1.29.09 in class-25% if late within 24 hours-50% if later than that 1. This problem aims to give you a flavor into the process of designing cars for an adventurous roller coaster ride. We can model the car as a single degree of freedom system subjected to a forcing function (this is due to the design of the roller coaster rails). As an example assuming that the governing equation is as follows Figure 1: Roller coaster design ¨ x + 9 ˙ x + 36 x = 54cos 3 t (a) Find the steady state response (otherwise known as the asymptotic or the particular solution) of the coaster car analytically i.e x ( t ). (b) While designing such rides, one of the important parameters is the rate of acceleration i.e ˙ a = ... x the person is subjected to. This rate is called jerk . Find the steady state jerk and compute its phase with respect to the force. ME163 Mechanical Vibrations 1 HW3 2. Consider a disk of mass m and radius r connected to a linear spring and to an arrangement of three...
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