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A mass weighing 16 lb stretches a spring 3 in. The mass is attached to a viscous damper with a damping constant of 2 lb - s/ft. If the mass is set in motion from its equilibrium position with a downward velocity of 2 in/s, find its position u at any time t. Assume the acceleration of gravity g = 32 ft/s². u u= u= 1 √31 1 12√31 1 1 12√31 1 √31 1 e-2¹ sin2 √/31t √3-2 sin 31 'cos2√311 + 21 cos2√√/31t "sin2√31t -21 sin2√31t cos2√31t

A mass weighing 16 lb stretches a spring 3 in. The mass is attached to a viscous damper with a damping constant of 2 lb - s/ft. If the mass is set in motion from its equilibrium position with a downward velocity of 2 in/s, find its position u at any time t. Assume the acceleration of gravity g = 32 ft/s². u u= u= 1 √31 1 12√31 1 1 12√31 1 √31 1 e-2¹ sin2 √/31t √3-2 sin 31 'cos2√311 + 21 cos2√√/31t "sin2√31t -21 sin2√31t cos2√31t

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 mass weighing 16 lb stretches a spring 3 in. The mass is attached to a viscous damper with a damping constant of 2 lb - s/ft. If the mass is set in motion from its equilibrium position with a downward velocity of 2 in/s, find its position u at any time t. Assume the acceleration of gravity g = 32 ft/s². u = 11 = u = √31 1 -21 cos2√31t+ 12√/31 1 e-2¹ sin2 √/31t √31 1 12√31 1 e-2¹ cos2√√/31t √31 1 12√31 -2⁰ sin2√31t -2¹ cos2√√31t 1 e-21 sin2 v √√31 2√√/31t 1 -e -2¹ cos2√√/31t+ e-2¹ sin2√31t 12√/31
Transcribed Image Text:A mass weighing 16 lb stretches a spring 3 in. The mass is attached to a viscous damper with a damping constant of 2 lb - s/ft. If the mass is set in motion from its equilibrium position with a downward velocity of 2 in/s, find its position u at any time t. Assume the acceleration of gravity g = 32 ft/s². u = 11 = u = √31 1 -21 cos2√31t+ 12√/31 1 e-2¹ sin2 √/31t √31 1 12√31 1 e-2¹ cos2√√/31t √31 1 12√31 -2⁰ sin2√31t -2¹ cos2√√31t 1 e-21 sin2 v √√31 2√√/31t 1 -e -2¹ cos2√√/31t+ e-2¹ sin2√31t 12√/31
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