w Explanation Given information: The weightis 16 lb , the velocity is 8 ft s and the stretch of spring is 8 in . Calculation: Consider the equation. m = W g = 16 32 = 0.5 The spring constant is, m g = k x 16 = k 8 12 k = 24 According to Hook’s law. m x ″ ( t ) = − k x ( t ) m x ″ ( t ) + k x ( t ) = 0 The solution of above equation is, x ( t ) = C 1 cos k m t + C 2 sin k m t x ( t ) = C 1 cos 4 3 t + C 2 sin 4 3 t …… (1) Differentiate above equation. x ′ ( t ) = 4 3 ( − C 1 sin 4 3 t + C 2 cos 4 3 t ) ……

Calculus: Special Edition: Chapters 1-5 (w/ WebAssign)

6th Edition

ISBN: 9781524908102

Author: SMITH KARL J, STRAUSS MONTY J, TODA MAGDALENA DANIELE

Publisher: Kendall Hunt Publishing

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Chapter 14.2, Problem 39PS

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Chapter 14.2, Problem 38PS

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2. Coasting battleship Suppose that an Iowa class battleship has mass around 51,000 metric tons (51,000,000 kg) and a k value in Equation (1) of about 59,000 kg/sec. Assume that the ship loses power when it is moving at a speed of 9 m/sec. a. About how far will the ship coast before it is dead in the water? b. About how long will it take the ship's speed to drop to 1 m/sec?

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Calculus: Special Edition: Chapters 1-5 (w/ WebAssign)

Ch. 14.1 - Prob. 1PS Ch. 14.1 - Prob. 2PS Ch. 14.1 - Prob. 3PS Ch. 14.1 - Prob. 4PS Ch. 14.1 - Prob. 5PS Ch. 14.1 - Prob. 6PS Ch. 14.1 - Prob. 7PS Ch. 14.1 - Prob. 8PS Ch. 14.1 - Prob. 9PS Ch. 14.1 - Prob. 10PS

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The formula for the position of weight as a function of time.

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