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A 64 pound weight is attached to the lower end of a coiled spring suspended from...

A 64 pound weight is attached to the lower end of a coiled spring suspended from the ceiling. The weight comes to rest at its equilibrium position, thereby stretching the spring 1/2 foot. At time t = 0, the weight is positioned 1 /√3 feet below equilibrium and given a downward velocity of 8 feet per second.

(a) Determine the equation of motion of the weight as a function of time.

(b) Find the amplitude of the motion.

(c) Find the period of the motion.

(d) Find the phase angle.

(e) Determine the times that the weight passes through equilibrium.

(f) Determine the third time the weight passes through equilibrium moving upward.

(g) Determine the second time the weight passes through equilibrium moving downward.

(h) Determine the times the weight is 1 foot below equilibrium.

(i) Determine the second time the weight is 1 foot below equilibrium moving upward.

(j) Determine the second time the weight is 1 foot below equilibrium moving downward

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