Explanation Given: Mass of each color is m and spring constant is k . Concept used: Energy conservation of the system is given as follows: ∑ K E + ∑ P E = constant ........ (1) Here, total kinetic energy is ∑ K E and total potential energy is ∑ P E . Calculation: Kinetic diagram of the system is given as follows: Taking moment about point D as follows: ∑ M D = 0 m g 2 × l 2 − k u ( 3 l 2 ) = 0 u = m g 2 3 k Natural length is calculated as follows: l o = l + u Total potential energy is calculated as follows: ∑ P E = 1 2 k ( ( l − 2 x ) − l o ) 2 + m g y ∑ P E = 1 2 k ( ( l − 2 x ) − l − u ) 2 + m g ( ( 1 3 ) x − ( 4 3 3 l ) x 2 ) ∑ P E = ( 2 k + 4 m g 3 3 l ) x 2 + constant ∑ P E = ( 2 k + 4 m g 3 3 l ) x 2 Total kinetic energy is calculated as follows: ∑ K E = 2 ( 1 2 ) m x ˙ 2 + 1 2 m y ˙ 2 ∑ K E = m x ˙ 2 + 1 2 m ( x ˙ 3 ) 2 ∑ K E = 7 m 6 x ˙ 2 Substitute ( 2 k + 4 m g 3 3 l ) x 2 for ∑ P E and 7 m 6 x ˙ 2 for ∑ K E in equation (1)

Vector Mechanics for Engineers: Dynamics

11th Edition

ISBN: 9780077687342

Author: Ferdinand P. Beer, E. Russell Johnston Jr., Phillip J. Cornwell, Brian Self

Publisher: McGraw-Hill Education

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Whenever an object/system displaces in either side of its equilibrium position with the help of an external/internal means, then the object/system moves regularly or randomly on both sides of its equilibrium position. This motion is called vibration. Gen…

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Chapter 19.3, Problem 19.96P

To determine

The frequency of vibration.

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Chapter 19.3, Problem 19.95P

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The frequency of vibration.

Solution Summary: The author calculates the energy conservation of the system by calculating the mass of each color and the spring constant.

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