hw4_solu

hw4_solu - ME163 Mechanical Vibrations (Winter 2009) Due...

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ME163 Mechanical Vibrations (Winter 2009) Due Wednesday 2.4.09 7pm (in the box or to a TA) Worth 75 Extra Credit points Answers emailed by 9pm, midterm the day after 1. Consider the system in Fgure below, with m eff = 20 [kg], damping coe±cient c = 500 [Ns/m] and spring sti²ness k = 2000 [N/m]. Suppose the system is forced by a sinusoidal force f ( t ) = 350cos ωt . You may neglect gravity. (a) Derive the equation of motion for the length of the spring (ie the distance between the mass and the connection point for the spring/damper). (b) Calculate the steady state response of the spring length at ω = 10 [rad/s] using phasors. k m c f Let us call F d the force of the damper, and F s the force of the spring. ³urthermore, let us call k m c x_d x_s F_d F_s distances x d and x s as in Fgure, and let x s 0 be the unstretched length of the spring. Being damper and spring in series, we have F d = F s . Then m x d + ¨ x s ) = F s = k ( x s x s 0 ) , ME163 Mechanical Vibrations 1 HW4
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hw4_solu - ME163 Mechanical Vibrations (Winter 2009) Due...

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