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pset5sol

# pset5sol - ME3015 PROBLEM SET#5(25 points Solutions 1(6...

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ME3015 PROBLEM SET #5 (25 points). Solutions 1. (6 points) A free vibration of the mass-spring-damper system shown below indicates that the amplitude of vibration decreases 25% after four cycles of motion. Find the viscous coefficient b when m =1[kg] and k =500[N/m]. (a) (b) m=1;k=500;b=2.46;G=tf(1,[m b k]);impulse(G) 2. Write the governing equations for the following mechanical system with two inputs ( u 1 (t) and u 2 (t)) and two outputs ( x 1 (t) and x 2 (t)). Put these equations in vector-matrix form and obtain the state-space representation of the mechanical system. x 1 (t) and x 2 (t) are measured from static equilibrium points.

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Solution Dynamic equations 1 1 2 2 1 1 1 2 2 1 1 1 1 ) ( ) ( u x x b x b x x k x k x m 2 1 2 2 1 2 2 2 2 ) ( ) ( u x x b x x k x m 2 nd order ODE, two variables Need 4 state variables Define    T x x x x z z z z 2 2 1 1 4 3 2 1 x .
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pset5sol - ME3015 PROBLEM SET#5(25 points Solutions 1(6...

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