Explanation Given information: The mass of the sphere A and C is m . The spring constant is k . Calculation: Write the expression for mass moment of inertia ( I ¯ ) : I ¯ B = m l 2 + m ( l 2 ) 2 Write the expression for displacement ( x ): x = l 2 θ Write the expression for kinetic energy ( T ): T = 1 2 I ¯ B θ ˙ 2 Substitute m l 2 + m ( l 2 ) 2 for I ¯ B . T = 1 2 ( m l 2 + m ( l 2 ) 2 ) θ ˙ 2 Write the expression for potential energy ( V ): V = 1 2 k x 2 Substitute l 2 θ for x . V = 1 2 k ( l 2 θ ) 2 = 1 2 k ( l θ 2 ) 2 = k l 2 8 θ 2 Calculate the total energy of the system using the relation: T + V = 0 Substitute k l 2 8 θ 2 for V and 1 2 ( m l 2 + m ( l 2 ) 2 ) θ ˙ 2 for T

12th Edition

ISBN: 9781260265453

Author: BEER

Publisher: MCG

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Forced undamped vibrations

In mechanical engineering, vibration is expressed as the term that occurs due to an object's backward and forward movement about a point of equilibrium. Generally, there are three types of vibrations which are,

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Chapter 19.3, Problem 19.70P

To determine

The frequency (fn) of the small oscillation of the system.

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Chapter 19.3, Problem 19.69P

Chapter 19.3, Problem 19.71P

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The frequency ( f n ) of the small oscillation of the system.

Solution Summary: The author calculates the expression for mass moment of inertia, kinetic energy, and potential energy.

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The frequency (fn) of the small oscillation of the system.

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