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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. Determine the equation of motion if the mass is initially released from a point 1 meter below the equilibrium positon with an upward velocity of 12m/s. -2 -2t 5 8t

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. Determine the equation of motion if the mass is initially released from a point 1 meter below the equilibrium positon with an upward velocity of 12m/s. -2 -2t 5 8t

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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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. Determine the equation of motion if the mass is initially released from a point 1 meter below the equilibrium positon with an upward velocity of 12m/s. -2 u(t)= 5 .-2t -8t e + e 3 3 5 u(t)= = 1/²/3e-2t + -8t е e 3 O 5 |u(t)==-e-2t₁ -8t 3 Ⓒu(t)=²8-2 +²² = шыш
Transcribed Image Text: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. Determine the equation of motion if the mass is initially released from a point 1 meter below the equilibrium positon with an upward velocity of 12m/s. -2 u(t)= 5 .-2t -8t e + e 3 3 5 u(t)= = 1/²/3e-2t + -8t е e 3 O 5 |u(t)==-e-2t₁ -8t 3 Ⓒu(t)=²8-2 +²² = шыш
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