Answered: r(m/M)(@;/w,)² Хт 1 – (@/w,) Wn Vk/M.

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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A motor of mass M is supported by springs with an equivalent spring constant k The unbalance of its rotor is equivalent to a mass m located at a distance r from the axis of rotation. Show that when the angular velocity of the motor is wf, the amplitude of the motion of the motor is where

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Resolving forces in the vertical direction :

$M \ddot{x} = P_{m} \sin ω_{f} t - k x M \ddot{x} + k x = P_{m} \sin ω_{f} t \ddot{x} + \frac{k}{M} = \frac{P_{m} \sin ω_{f} t}{M} ω_{n} = \sqrt{\frac{k}{M}} {ω_{n}}^{2} = \frac{k}{M} k = M {ω_{n}}^{2}$

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