Explanation Draw the schematic diagram. Write the expression for the centroidal distance ( r ¯ ) . r ¯ = 2 l ( 1 2 l sin 60 ° ) + l ( l sin 60 ° ) 3 l r ¯ = l 3 (I) Here, the side of the triangle is l . Write the expression for the moment of inertia about BB axis ( I B B ) . I B B = 2 [ 1 3 ( ρ l ) ( l 2 ) ] + 1 12 ( ρ l ) ( l 2 ) + ( ρ l ) ( l sin 60 ° ) 2 I B B = 3 2 ρ l 3 (II) Here, the mass per unit length is ρ . Conclusion: Taking moment about the point O . ∑ M o = I B B θ ¨ − m g r ¯ sin θ = I B B θ ¨ (III) Substitute, Equation (I) and Equation (II) in Equation (III) . − 3 ρ g l ( l 3 ) sin θ = ( 3 2 ρ l 3 ) θ ¨ ( 3 2 ρ l 3 ) θ ¨ + 3 ρ g l ( l 3 ) sin θ = 0 (IV) Rewrite Equation (IV) for small values of θ

8th Edition

ISBN: 9781118885840

Author: James L. Meriam, L. G. Kraige, J. N. Bolton

Publisher: WILEY

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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 8.4, Problem 84P

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The natural circular frequency of the system.

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Chapter 8.4, Problem 83P

Chapter 8.4, Problem 85P

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