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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. (a) the mass is initially released from rest from a point 1 meter below the equilibrium position x(0) = x'(0) = -(6r) x(t) = c₂e x(t) = cos m m/s (√32)+c₂e m m/s -(6r), (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 √3.2 2 X m

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. (a) the mass is initially released from rest from a point 1 meter below the equilibrium position x(0) = x'(0) = -(6r) x(t) = c₂e x(t) = cos m m/s (√32)+c₂e m m/s -(6r), (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 √3.2 2 X m

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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. (a) the mass is initially released from rest from a point 1 meter below the equilibrium position x(0) = x'(0) = -(6t), x(t) = ₁₂e cos m m/s √3.2 2 m m/s -) + C₂²² -c₂e m -(6t) sin √3.2 2 (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) = X m
Transcribed Image Text: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. (a) the mass is initially released from rest from a point 1 meter below the equilibrium position x(0) = x'(0) = -(6t), x(t) = ₁₂e cos m m/s √3.2 2 m m/s -) + C₂²² -c₂e m -(6t) sin √3.2 2 (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) = X m
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