pset2_sol - ME3015 PROBLEM SET #2 (25 points). Document as...

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SOLUTIONS 1. (6 points) Solve the following differential equation of motion using Laplace Transform Techniques: 0 ) 0 ( , 5 ) 0 ( 0 4 x x x x   0 ) ( 4 ) 0 ( ) 0 ( ) ( 2 s X x sx s X s Substitution of the initial conditions gives 0 ) ( 4 5 ) ( 2 s X s s X s Solving for ) ( s X we obtain 4 5 ) ( 2 s s s X The inverse Laplace transform: t t x 2 cos 5 ) ( 2. (6 points) Find the natural frequency for the pendulum shown below. Assume small angle of motion. Solution 1 (easier) The horizontal posture shown in the figure is in static equilibrium. Gravity term can be dropped from the DEOM since the torque 3 2 L mg around the joint due to the point mass and the torque 3 L k by the spring balance where (constant) is the equilibrium spring deflection. g
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This note was uploaded on 02/08/2012 for the course ME 3015 taught by Professor Ueda during the Fall '08 term at Georgia Tech.

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pset2_sol - ME3015 PROBLEM SET #2 (25 points). Document as...

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