A cantilever is driven in flexural vibration by an electrical coil mounted at its free end and moving in the field of a magnet. The coil has been so designed that its mass is sufficiently small that it may be neglected but unfortunately this resulted in the moment of inertia of the coil being by no means negligible. For the beam, Young's modulus is E, the density is p its length is I and the second moment of inertia is I. The moment of inertia of the coil about an axis through its centre of gravity (which coincides with the end of the beam) perpendicular to the plane of vibration is J. Determine the frequency equation for this system.

A cantilever is driven in flexural vibration by an electrical coil mounted at its free end and moving in the field of a magnet. The coil has been so designed that its mass is sufficiently small that it may be neglected but unfortunately this resulted in the moment of inertia of the coil being by no means negligible. For the beam, Young's modulus is E, the density is p its length is I and the second moment of inertia is I. The moment of inertia of the coil about an axis through its centre of gravity (which coincides with the end of the beam) perpendicular to the plane of vibration is J. Determine the frequency equation for this system.

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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