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9. A 1-kg mass is attached to a spring whose constant is 16 N/m, and the entire system is then submerged in a liquid that imparts a damping force numerically equal to 10 times the instantaneous velocity. a. Determine the equation of motion if the mass is initially released from a point 1 meter below the equilibrium position with an upward velocity of 12 m/s. b. At what time does the mass reach its maximum displacement? (Hint: find critical point(s).)

9. A 1-kg mass is attached to a spring whose constant is 16 N/m, and the entire system is then submerged in a liquid that imparts a damping force numerically equal to 10 times the instantaneous velocity. a. Determine the equation of motion if the mass is initially released from a point 1 meter below the equilibrium position with an upward velocity of 12 m/s. b. At what time does the mass reach its maximum displacement? (Hint: find critical point(s).)

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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9. A 1-kg mass is attached to a spring whose constant is 16 N/m, and the entire system is then submerged in a liquid that imparts a damping force numerically equal to 10 times the instantaneous velocity. a. Determine the equation of motion if the mass is initially released from a point 1 meter below the equilibrium position with an upward velocity of 12 m/s. b. At what time does the mass reach its maximum displacement? (Hint: find critical point(s).)
Transcribed Image Text:9. A 1-kg mass is attached to a spring whose constant is 16 N/m, and the entire system is then submerged in a liquid that imparts a damping force numerically equal to 10 times the instantaneous velocity. a. Determine the equation of motion if the mass is initially released from a point 1 meter below the equilibrium position with an upward velocity of 12 m/s. b. At what time does the mass reach its maximum displacement? (Hint: find critical point(s).)
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