dsc_hw_4_w09 - Homework Set#4 MAE 3600 Dynamic Systems and...

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Homework Set #4: MAE 3600 – Dynamic Systems and Control, Winter 2009 Due date: Monday, March 2, 2009 Problem 1. A sensitive instrument platform for microgravity experiments onboard the Space Shuttle is mounted on shock mounts in order to reduce vibrational motion. The system (shown below) can be modeled as a simple mass-spring-damper system. The mass is m = 0.8 kg, total stiffness for the shock mount is k = 230 N/m, and total damping coefficient for the mount is b = 4 N-s/m. Vertical displacement z is measured from the static equilibrium position. The system inputs are base motion ( z 0 ) from pumps, fans, and astronaut motion; disturbance force ( F dist ) from electrical cords or motors mounted on the payload; and an active control force ( F act ) produced by an electromagnetic actuator. For this problem, assume that the two input forces F dist = F act = 0. a) Derive the transfer function for the instrument platform system. b) Obtain the analytical solution of the dynamic response using Laplace transform methods if the base motion input is an impulse: ) ( 006 . 0 ) ( 0 t t z δ = m. Assume
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This note was uploaded on 06/29/2011 for the course MAE 3600 taught by Professor Pai during the Spring '09 term at Missouri (Mizzou).

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dsc_hw_4_w09 - Homework Set#4 MAE 3600 Dynamic Systems and...

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