A 1-kilogram 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 initial conditions and equations of motion if the following is true. (a) the mass is initially released from rest from a point 1 meter below the equilibrium position x(0) = x'(0) - 4/3 x(t) = x m/s m (b) the mass is initially released from a point 1 meter below the equilibrium position with an upward velocity of 11 m/s x(0) = x'(0) = x(t) = m/s
A 1-kilogram 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 initial conditions and equations of motion if the following is true. (a) the mass is initially released from rest from a point 1 meter below the equilibrium position x(0) = x'(0) - 4/3 x(t) = x m/s m (b) the mass is initially released from a point 1 meter below the equilibrium position with an upward velocity of 11 m/s x(0) = x'(0) = x(t) = m/s
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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Transcribed Image Text:A 1-kilogram 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 initial conditions and equations of motion if the following is true.
(a) the mass is initially released from rest from a point 1 meter below the equilibrium position
x(0) =
x'(0) 4/3
x(t) =
m
x m/s
m
(b) the mass is initially released from point 1 meter below the equilibrium position with an upward velocity of 11 m/s
x(0) =
x'(0) =
x(t) =
m
m/s
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