Determine the equation of motion if the spring constant is 8 lb/ft and if the weight is released 15 inches above the equilibrium with a downward velocity of 18 inches/s. (a) (t)= preview (b) find the amplitude: preview (c) find the first time that the mass attains its extreme displacement: preview seconds (d) find the first time that the object is at its equilibrium position: seconds preview ft (d) find the velocity of the object when it's its equilibrium for the first time

Afaulty model rocket moves in the xy-plane (the positive y direction is vertically upward). the rocket's acceleration has components ax(t) = ? t2 and ay(t) = ? ? ? t, where ? = 2.50 m/s4 , ? = 9.00 m/s2 , and ? = 1.40 m/s3 . at t = 0 the rocket is at the origin and has velocity ~v0 = v0x ? i + v0y ? j with v0x = 1.00 m/s and v0y = 7.00 m/s. (a) calculate the velocity and position vectors as functions of time. (b) what is the maximum height reached by the rocket? (c) sketch the path of the rocket. (d) what is the horizontal displacement of the rocket when it returns to y = 0?