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A 4-foot spring measures 8 feet long after a mass weighing 8 pounds is attached to it. The medium through which the mass moves offers a damping force numerically equal to √2 times the instantaneous velocity. Find the equation of motion if the mass is initially released from the equilibrium position with a downward velocity of 7 ft/s. (Use g = 32 ft/s² for the acceleration due to gravity.) x(t) = 2.48e-0.08tsin (2.82t) X Find the time at which the mass attains its extreme displacement from the equilibrium position. t = 0.54 X What is the position of the mass at this instant? The extreme displacement is x = 2.37 X feet.

A 4-foot spring measures 8 feet long after a mass weighing 8 pounds is attached to it. The medium through which the mass moves offers a damping force numerically equal to √2 times the instantaneous velocity. Find the equation of motion if the mass is initially released from the equilibrium position with a downward velocity of 7 ft/s. (Use g = 32 ft/s² for the acceleration due to gravity.) x(t) = 2.48e-0.08tsin (2.82t) X Find the time at which the mass attains its extreme displacement from the equilibrium position. t = 0.54 X What is the position of the mass at this instant? The extreme displacement is x = 2.37 X feet.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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A 4-foot spring measures 8 feet long after a mass weighing 8 pounds is attached to it. The medium through which the mass moves offers a damping force numerically equal to √2 times the instantaneous velocity. Find the equation of motion if the mass is initially released from the equilibrium position with a downward velocity of 7 ft/s. (Use g = 32 ft/s² for the acceleration due to gravity.) x(t) = 2.48e-0.08tsin (2.82t) X Find the time at which the mass attains its extreme displacement from the equilibrium position. t = 0.54 X What is the position of the mass at this instant? The extreme displacement is x = 2.37 X feet.
Transcribed Image Text:A 4-foot spring measures 8 feet long after a mass weighing 8 pounds is attached to it. The medium through which the mass moves offers a damping force numerically equal to √2 times the instantaneous velocity. Find the equation of motion if the mass is initially released from the equilibrium position with a downward velocity of 7 ft/s. (Use g = 32 ft/s² for the acceleration due to gravity.) x(t) = 2.48e-0.08tsin (2.82t) X Find the time at which the mass attains its extreme displacement from the equilibrium position. t = 0.54 X What is the position of the mass at this instant? The extreme displacement is x = 2.37 X feet.
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