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 equations of motion if the following is true. (Show a sketch of the problem) (a) the mass is initially released from rest from a point 1 meter below the equilibrium position (b) the mass is initially released from a point 1 meter below the equilibrium position with an upward velocity of 12 m/s (c) In parts a and b of the problem, determine whether the mass passes through the equilibrium position. In each case find the time at which the mass attains its extreme displacement from the equilibrium position. What is the position of the mass at this instant?
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 equations of motion if the following is true. (Show a sketch of the problem)
(a) the mass is initially released from rest from a point 1 meter below the equilibrium position
(b) the mass is initially released from a point 1 meter below the equilibrium position with an upward velocity of 12 m/s
(c) In parts a and b of the problem, determine whether the mass passes through the equilibrium position. In each case find the time at which the mass attains its extreme displacement from the equilibrium position. What is the position of the mass at this instant?
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