dsc_hw1_w09 - Homework Set#1 MAE 3600 Dynamic Systems and...

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Homework Set #1: MAE 3600 – Dynamic Systems and Control, Winter 2009 Due date: Monday, February 2, 2009 Problem 1. A mechanical system is shown below. The connecting rod has moment of inertia J about its pivot point, and rotation angle θ is positive clockwise. Position of mass m is positive to the right. Both the angular and translational displacements are measured from the equilibrium position where all springs are undeflected. a) Derive the complete (nonlinear) mathematical model for this system. Show all steps. b) Derive a linear model for this system and show all steps. Problem 2. A simple rotational mechanical system consists of a rotor (disk) with moment of inertia J = 0.2 kg-m 2 . The rotor and its bearings are in a cylindrical case that is filled with a hydraulic fluid, and the resulting friction torque can be modeled by viscous friction coefficient b = 0.014 N-m-s/rad. At time t = 0, the rotor has an angular velocity of 250 rpm (rev/min). a)
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dsc_hw1_w09 - Homework Set#1 MAE 3600 Dynamic Systems and...

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