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.

International Edition---engineering Mechanics: Statics, 4th Edition

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ISBN:9781305501607

Author:Andrew Pytel And Jaan Kiusalaas

Publisher:Andrew Pytel And Jaan Kiusalaas

Chapter5: Three-dimensional Equilibrium

Section: Chapter Questions

Problem 5.15P: In Sample Problem 5.5, determine Oy with one scalar equilibrium equation.

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Concept explainers

Basic Terminology in Mechanics

The area of science and mathematics concerned the motion of the objects, the relation between the force matter, and motion if specified. Forces exerted over the objects result in displacements or changes in the position of an object concerning its environment. This branch of physics keeps its roots in Ancient Greece in the form of the scripts of Aristotle and Archimedes.

Question

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.

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