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mech_inclass - Translational Mechanical Systems Rotational...

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Translational Mechanical Systems Rotational Mechanical Systems Unit 2: Modeling in the Frequency Domain Part 5: Modeling Mechanical Systems Engineering 5821: Control Systems I Faculty of Engineering & Applied Science Memorial University of Newfoundland January 30, 2009 ENGI 5821 Unit 2, Part 5: Modeling Mechanical Systems
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Translational Mechanical Systems Rotational Mechanical Systems 1 Translational Mechanical Systems Example: Via DE Example: Problem Stated in the Freq. Domain Linearly Independent Motions 1 Rotational Mechanical Systems Gears ENGI 5821 Unit 2, Part 5: Modeling Mechanical Systems
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Translational Mechanical Systems We will model mechanical systems using three components:
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Translational Mechanical Systems We will model mechanical systems using three components: Spring: A spring applies a force against compression/expansion Mass: A moving mass has inertia and resists changes in velocity Viscous Damper: Resists motion (pure energy loss)
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Analogies with electrical quantities: Force is analagous to voltage, velocity to current, and displacement to charge.
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Analogies with electrical quantities: Force is analagous to voltage, velocity to current, and displacement to charge. Analogies with electrical components: Spring Capacitor, Mass Inductor, Viscous Damper Resistor
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Example: Via DE Find the transfer function X ( s ) / F ( s ) for the following system,
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Example: Via DE Find the transfer function X ( s ) / F ( s ) for the following system, Assume the mass is travelling to the right, pulled by the force f ( t ).
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Example: Via DE Find the transfer function X ( s ) / F ( s ) for the following system, Assume the mass is travelling to the right, pulled by the force f ( t ). All other forces oppose this motion.
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Example: Via DE Find the transfer function X ( s ) / F ( s ) for the following system, Assume the mass is travelling to the right, pulled by the force f ( t ). All other forces oppose this motion. Draw the free body diagram:
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Example: Via DE Find the transfer function X ( s ) / F ( s ) for the following system, Assume the mass is travelling to the right, pulled by the force f ( t ). All other forces oppose this motion. Draw the free body diagram:
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Example: Via DE Find the transfer function X ( s ) / F ( s ) for the following system, Assume the mass is travelling to the right, pulled by the force f ( t ). All other forces oppose this motion. Draw the free body diagram: The sum of forces must equal zero,
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Example: Via DE Find the transfer function X ( s ) / F ( s ) for the following system, Assume the mass is travelling to the right, pulled by the force f ( t ). All other forces oppose this motion. Draw the free body diagram: The sum of forces must equal zero, M d 2 x ( t ) dt 2 + f v dx ( t ) dt + Kx ( t ) = f ( t )
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Example: Via DE Find the transfer function X ( s ) / F ( s ) for the following system, Assume the mass is travelling to the right, pulled by the force f ( t ).
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