Explanation Consider the equation for position of point A . s = 2 b sin θ (I) Differentiate Equation (I) with respect to time to get, v = 2 b θ ˙ cos θ (II) Again Differentiate Equation (II) with respect to time to get, a = 2 b ( θ ¨ cos θ − θ ˙ 2 sin θ ) The value of θ is very small. Hence, sin θ is negligible. a = 2 b ( θ ¨ cos θ − 0 ) = 2 b θ ¨ cos θ Compute the change in potential energy of link A C . Δ P E A C = ( P cos θ ) d ( 2 b sin θ ) Compute the change in potential energy of link O C . Δ P E O C = P b d θ Compute the rotational and translational kinetic energy of link A C . Δ K E A C = d [ 1 2 ( 2 m ) v 2 + 1 2 I ω 2 ] = 2 m v d v + I ω d ω = 2 m a d s + I α d θ = 2 m ( 2 b θ ¨ cos θ ) d ( 2 b sin θ ) + [ 1 12 ( 2 m ) ( 2 b ) 2 × θ ¨ d θ ] = 2 m b 2 [ 4 cos 2 θ + 1 3 ] θ ¨ d θ Compute the rotational kinetic energy of link O C . Δ K E O C = d [ 1 2 I O C ω 2 ] = I O C ω d ω = I O C α d θ = 1 3 m b 2 θ ¨ d θ Apply conservation of energy principle

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 6.7, Problem 158P

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Determine the initial angular acceleration of the links.

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Chapter 6.7, Problem 157P

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