# Assignment1 - Instructor:Dr.EmreAlpman Assignment#1 DueDate:February25th,2010 ProblemStatement FrictionForce L/2=lCG mg Figure1.Schematicdia

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ME 472 Computer-Aided Mechanical Engineering Instructor: Dr. Emre Alpman Assignment #1 Due Date: February 25th, 2010 SINGLE DEGREE-OF-FREEDOM SYSTEMS Problem Statement Consider a pendulum which can rotate about its end as shown in Figure 1. Figure 1. Schematic diagram of the model. The pendulum has a length of 25 cm and a weight of 25 kg. When the pendulum is rotated from the  equilibrium point by an amount   θ   , the weight of the pendulum will try to bring it back to the  equilibrium position. Also the friction at the joint generates a damping force which is proportional to  and in the reverse direction of the angular speed of the disk. The equation of rotational motion can be  written as: I ¨ θ =− mgl G sin θ c ˙ θ Where   I   is the mass moment of inertia,   m   is the mass,   c   is the damping constant and   g   is the  θ mg Friction Force L /2 =  l CG

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gravitational   acceleration.   The   above   equation   is   nonlinear.   If   we   make   a   small   displacement  assumption we can write  sin θ θ . Then the equation of motion becomes: I ¨ θ c ˙ θ mg l G θ = 0 With initial conditions  θ 0 = 10 deg. and  ˙ θ 0 = 0 . Damping constant  c  is taken as: 2 N-s/m.  Lab Assignment It is asked to solve for the dynamics of this model in time, using both analytical  and numerical  approaches, and a comparison between the two approaches be offered. Numerical Solution A modular and flexible programming approach is adopted in this assignment,  and students will be  encouraged to continue using this approach throughout the course. When designing a numerical
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## This note was uploaded on 04/05/2012 for the course MECHANICAL ME372 CAME taught by Professor Emraalpman during the Spring '10 term at Yeditepe Üniversitesi.

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Assignment1 - Instructor:Dr.EmreAlpman Assignment#1 DueDate:February25th,2010 ProblemStatement FrictionForce L/2=lCG mg Figure1.Schematicdia

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