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2. A mass that weighs 64 lb stretches a spring 0.8 ft. The mass is attached to a dashpot mechanism that has a damping coefficient of 8 lb s/ft and is acted on by an external force of 60 cos(4t) lb. The mass is set in motion from its equilibrium position with no initial velocity. Let y(t) denote the displacement (in ft) of the mass from its equilibrium position after t seconds. (a) Find an initial-value problem which describes this process. (You may use the fact that g = 32 ft/s? and 1 ft=12 in.) (b) Is the system underdamped, overdamped, or critically damped? Justify your an- Swer.

2. A mass that weighs 64 lb stretches a spring 0.8 ft. The mass is attached to a dashpot mechanism that has a damping coefficient of 8 lb s/ft and is acted on by an external force of 60 cos(4t) lb. The mass is set in motion from its equilibrium position with no initial velocity. Let y(t) denote the displacement (in ft) of the mass from its equilibrium position after t seconds. (a) Find an initial-value problem which describes this process. (You may use the fact that g = 32 ft/s? and 1 ft=12 in.) (b) Is the system underdamped, overdamped, or critically damped? Justify your an- Swer.

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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2. A mass that weighs 64 lb stretches a spring 0.8 ft. The mass is attached to a dashpot mechanism that has a damping coefficient of 8 lb s/ft and is acted on by an external force of 60 cos(4t) lb. The mass is set in motion from its equilibrium position with no initial velocity. Let y(t) denote the displacement (in ft) of the mass from its equilibrium position after t seconds. (a) Find an initial-value problem which describes this process. (You may use the fact that g = 32 ft/s' and 1 ft=12 in.) (b) Is the system underdamped, overdamped, or critically damped? Justify your an- swer.
Transcribed Image Text:2. A mass that weighs 64 lb stretches a spring 0.8 ft. The mass is attached to a dashpot mechanism that has a damping coefficient of 8 lb s/ft and is acted on by an external force of 60 cos(4t) lb. The mass is set in motion from its equilibrium position with no initial velocity. Let y(t) denote the displacement (in ft) of the mass from its equilibrium position after t seconds. (a) Find an initial-value problem which describes this process. (You may use the fact that g = 32 ft/s' and 1 ft=12 in.) (b) Is the system underdamped, overdamped, or critically damped? Justify your an- swer.
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