A mass weighing 8 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.
A mass weighing 8 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.
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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Transcribed Image Text:A mass weighing 8 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/s?.
1
U =
cond Vi + sintv
1
4' sin4 /7t
1
cos4 7t +
24
u =
sin4 7t
24V7
V7
1
A cos4/7t
U =
24V7
'cos47t
V7
1
4i sin4 7t
247
1
"sin4 /īt
u =
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