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# OMU 324-HW3 - • • where u= f(t is the input force and...

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OMU 324 System Dynamics & Control Homework #3 Due Date: 29/03/2010 1) Linearize the non-linear system given below by using state space method. ) cos( ) sin( 2 u y y y y = + + + 2) Mass-spring- damper system given below consists of two masses “M,m”, one linear spring with a stiffness of “k1”, one damper with a damping coefficient of “c” and one non-linear spring which is defined 3 1 2 2 ) ( x x k f k - = . The table will be useful to solve the problem. a) Show that the equations of motion are; 3 1 2 2 2 ) ( ) ( x x k t f x m - - = 1 1 3 1 2 2 1 ) ( kx x c x x k x M - - -
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Unformatted text preview: • • , where u= f(t) is the input force and x1&x2 are the positions. b) Linearize the system about u=0. c) Simulate the linearized system and non-linearized system for: 1. A sinusoidal input of small amplitude 2. A sinusoidal input of large amplitude 3. Comment on your observations in part (a) and part (b). HACETTEPE UNIVERSITY Mechanical Engineering Department Parameters Value f(t) u(t), input x1(t), x2(t) output k1 10 N/m k2 1 N/m M 10 kg m 1 kg c 1 Ns/m...
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