Explanation Given information: Mass of each block m = 1.5 Κ g Spring constant k = 720 Ν / m Initial velocity v = 250 m m / s Concept used: By using the principle of conservation of energy for the free vibration of un-damped system, the energy is partly kinetic and partly potential, keeping the total energy being constant. Thus, T + V = Constant Kinetic energy of the system T = 1 2 m ( b 2 + c 2 ) θ ˙ 2 And,Potential energy of the system V = 1 2 k c 2 θ 2 Calculation: Total energy = kinetic energy + Potential energy 1 2 m ( b 2 + c 2 ) θ ˙ 2 + 1 2 k c 2 θ 2 = 0 Now, differentiating the above equation with respect to time (t) to find the natural frequency. Thus, d d t [ 1 2 m ( b 2 + c 2 ) θ ˙ 2 + 1 2 k c 2 θ 2 ] = 0 d d t [ 1 2 m ( b 2 + c 2 ) θ ˙ 2 ] + d d t [ 1 2 k c 2 θ 2 ] = 0 1 2 m ( b 2 + c 2 ) [ 2 θ ¨ . θ ˙ ] + 1 2 k c 2 2 θ ˙ . θ = 0 m ( b 2 + c 2 ) θ ¨

12th Edition

ISBN: 9781259977305

Author: BEER, Ferdinand P. (ferdinand Pierre), Johnston, E. Russell (elwood Russell), Cornwell, Phillip J., SELF, Brian P.

Publisher: Mcgraw-hill Education,

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Forced undamped vibrations

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Chapter 19.3, Problem 19.69P

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The magnitude of maximum displacement of block D.

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Chapter 19.2, Problem 19.68P

Chapter 19.3, Problem 19.70P

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Two blocks each have a mass 1.5 kg and are attached to links that are pin-connected to bar BC as shown. The masses of the links and bar are negligible, and the blocks can slide without friction. Block D is attached to a spring of constant = 720 N/m. Knowing that bloc k = 720 N/m. Knowing that block A is at rest when it is struck horizontally with a mallet and given an initial velocity of 250 mm/s, determine the magnitude of the maximum displacement of block D during the resulting motion.

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The magnitude of maximum displacement of block D.

Solution Summary: The author explains the principle of conservation of energy for the free vibration of un-damped system.

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