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 \(\sqrt{2}\) 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 \(g = 32 \, \text{ft/s}^2\) for the acceleration due to gravity.)\(x(t) = \_\_\_\_\_\_\)Find the time at which the mass attains its extreme displacement from the equilibrium position.\(t = \_\_\_\_\_\_\)What is the position of the mass at this instant?The extreme displacement is \(x = \_\_\_\_\_\_\) feet.

Given- A 4-foot spring measures 8 feet long after a mass weighing 8 pounds is attached to it. The…

Answered: A 4-foot spring measures 8 feet long…

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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Find the position of the mass after t seconds
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