A 1-kilogram mass is attached to a spring whose constant is 27 N/m, and the entire system is then submerged in a liquid that imparts a damping force numerically equal to 12 times the instantaneous velocity. Determine the initial conditions and equations of motion ifthe following is true.(a) the mass is initially released from rest from a point 1 meter below the equilibrium positionx(0) =x'(0) =x(t) = C₁e-(6t)cosmm/s√3.221/²) + C₂m/sm61sin√3.22x(b) the mass is initially released from a point 1 meter below the equilibrium position with an upward velocity of 13 m/sx(0) =x'(0) =x(t) =m

For the given problem, First we write the differential equationGiven thatm=1 kg, c=27 n/m and…

Answered: A 1-kilogram mass is attached to a…

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-kilogram mass is attached to a spring whose constant is 27 N/m, and the entire system is then submerged in a liquid that imparts a damping force numerically equal to 12 times the instantaneous velocity. Determine the initial conditions and equations of motion if the following is true.