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C/G An 8 lb weight stretches a spring 1.5 inches. It is attached to a dashpot with damping constant c=8 lb-sec/ft. The weight is initially displaced 3 inches above equilibrium and given an upward velocity of 6 ft/sec. Find and graph its displacement for t > 0.

C/G An 8 lb weight stretches a spring 1.5 inches. It is attached to a dashpot with damping constant c=8 lb-sec/ft. The weight is initially displaced 3 inches above equilibrium and given an upward velocity of 6 ft/sec. Find and graph its displacement for t > 0.

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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**Exercise on Spring-Mass-Damper Systems** **3.** An 8 lb weight stretches a spring 1.5 inches. It is attached to a dashpot with a damping constant \( c = 8 \) lb-sec/ft. The weight is initially displaced 3 inches above equilibrium and given an upward velocity of 6 ft/sec. Find and graph its displacement for \( t > 0 \). **4.** A 96 lb weight stretches a spring 3.2 ft in equilibrium. It is attached to a dashpot with a damping constant \( c = 18 \) lb-sec/ft. The weight is initially displaced 15 inches below equilibrium and given a downward velocity of 12 ft/sec. Find its displacement for \( t > 0 \). --- *Instructions:* Analyze the dynamic behavior of these spring-mass-damper systems using differential equations. Derive the equations of motion based on the given initial conditions and solve them to determine the displacement over time. Provide graphical representations of the displacement for positive values of \( t \).
Transcribed Image Text:**Exercise on Spring-Mass-Damper Systems** **3.** An 8 lb weight stretches a spring 1.5 inches. It is attached to a dashpot with a damping constant \( c = 8 \) lb-sec/ft. The weight is initially displaced 3 inches above equilibrium and given an upward velocity of 6 ft/sec. Find and graph its displacement for \( t > 0 \). **4.** A 96 lb weight stretches a spring 3.2 ft in equilibrium. It is attached to a dashpot with a damping constant \( c = 18 \) lb-sec/ft. The weight is initially displaced 15 inches below equilibrium and given a downward velocity of 12 ft/sec. Find its displacement for \( t > 0 \). --- *Instructions:* Analyze the dynamic behavior of these spring-mass-damper systems using differential equations. Derive the equations of motion based on the given initial conditions and solve them to determine the displacement over time. Provide graphical representations of the displacement for positive values of \( t \).
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