In Figure a motor supplies a torque T to turn a drum of radius R and inertia

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In Figure a motor supplies a torque T to turn a drum of radius R and inertia I about its axis of rotation. The rotating drum lifts a mass m by means of a cable that wraps around the drum. The drum's speed is ω. viscous tensional damping cT exists in the drum shaft. Neglect the mass of the cable,
(a) Obtain the equation of motion with the torque T as the input and the vertical speed v of the mass as the output,
(b) Suppose that m = 40 kg, R = 0.2 m, I = 0.8 kg.m2, and cT = 0.1 N.m.s. Find the speed v(t) if the system is initially at rest and the torque T is a step function of magnitude 300 N.m.
In Figure a motor supplies a torque T to turn
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System Dynamics

ISBN: 978-0073398068

3rd edition

Authors: William Palm III

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