A 19 kg weight is attached to a spring with constant k = 475 kg/m and subjected to an external force F ( t ) = 1197 sin ( 2 t ) . The weight is initially displaced 2 meters above equilibrium and given an upward velocity of 3 m/s. Find its displacement for t > 0, with y ( t ) measured positive upwards.

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initial speed when it is dropped is 150 ft/s

now at the same moment the acceleration due to gravity is perpendicular to its velocity

so as we know that

now we have centripetal acceleration a = 32 ft/s^2 as its perpendicular to velocity

while tangential acceleration at the same moment will be zero

so

now radius of curvature is given as

so the radius of curvature just after it is dropped is 703.125 ft