Day #
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Lectures
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Topics
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1-3
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Brief Review of 2.003
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Uniaxial motion, fixed-axis rotation; first and second order systems; natural and forced response; transfer functions, zeroes, poles; elementary control: open-loop, closed-loop; closing the loop alters the natural and forced response characteristics; stability and instability.
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4-5
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Impulse Response
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Collisions; conservation of momentum; conservation of energy; coefficient of restitution; bouncing ball in the presence of air drag.
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6-9
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Plane-motion Kinematics of Rigid Bodies
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Combined translation and rotation of rigid body; angular velocity; generalized coordinates; common constraints. Kinetic energy of rigid body.
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10-15
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Plane-motion Dynamics of Rigid Bodies
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Linear and angular momentum principles for systems including rigid bodies; derivingequations of motion using momentum principles; conservation of energy; linearization in the neighbourhood of equilibrium, stability and instability; rolling cylinder inside rollinghoop; inverted pendulum on cart.
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16-18
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Vibrations of Two-Degree-of-Freedom Systems
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Natural modes and the eigenvalue problem; free and forced response to harmonic excitation; damping effects; Bode plots.
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19-24
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Control of Systems with Rigid Bodies
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Actuators, sensors; P, D, I feedback-loop strategies; root-locus design; application to inverted pendulum on cart, automatic self-balancing scale; frequency-domain design methods, gain margin, phase margin.
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