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

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter6: Vector Spaces
Section6.7: Applications
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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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