A 1-kilogram mass is attached to a spring whose constant is 14 N/m, and the entire system is then submerged in a liquid that imparts a damping force numerically equal to 9 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 point 1 meter below the equilibrium position x(0) = x'(0) = x(t) = m m/s x(t) = m (b) the mass is initially released from a point 1 meter below the equilibrium position with an upward velocity of 13 m/s x(0) = x'(0) = m m/s m

Advanced Engineering Mathematics
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Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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A 1-kilogram mass is attached to a spring whose constant is 14 N/m, and the entire system is then submerged in a liquid that imparts a damping force numerically equal to 9 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)
=
x(t) =
=
m/s
(b) the mass is initially released from a point 1 meter below the equilibrium position with an upward velocity of 13 m/s
x(0) =
x'(0)
x(t) =
m
m
m/s
m
Transcribed Image Text:A 1-kilogram mass is attached to a spring whose constant is 14 N/m, and the entire system is then submerged in a liquid that imparts a damping force numerically equal to 9 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) = x(t) = = m/s (b) the mass is initially released from a point 1 meter below the equilibrium position with an upward velocity of 13 m/s x(0) = x'(0) x(t) = m m m/s m
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