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Math / Differential Equations and Their Applications: An Introduction to Applied Mathematics 3 / Chapter 2.6 / Problem 11

Differential Equations and Their Applications: An Introduction to Applied Mathematics | 3rd Edition | ISBN: 9780387908069 | Authors: M. Braun

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A 1 kg mass is attached to a spring with spring constant k = 4 N/m, and hangs in

Chapter 2, Problem 11

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QUESTION:

A 1 kg mass is attached to a spring with spring constant k = 4 N/m, and hangs in equilibrium. An external force F(t) = (1 + t +sin2t) N is applied to the mass beginning at time t = 0. If the spring is stretched a length (1/2+ ~/4) m or more from its equilibrium position, then it will break. Assuming no damping present, find the time at which the spring breaks.

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QUESTION:

A 1 kg mass is attached to a spring with spring constant k = 4 N/m, and hangs in equilibrium. An external force F(t) = (1 + t +sin2t) N is applied to the mass beginning at time t = 0. If the spring is stretched a length (1/2+ ~/4) m or more from its equilibrium position, then it will break. Assuming no damping present, find the time at which the spring breaks.

ANSWER:

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Given:- A mass is attached to a spring with spring constant , and hangs in equilibrium. An external force is applied to the mass beginning at time . If the spring is stretched a length or more from its equilibrium position, then it will break.

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