Aweight attached to a spring is at its lowest point, 9 inches below equilibrium, at time t = 0 seconds. when the weight it released, it oscillates and returns to its original position at t = 3 seconds. which of the following equations models the distance, d, of the weight from its equilibrium after t seconds?

The motion can be modeled as

where 
x = the position below the equilibrium position
T =  the period of the motion
t = time

The weight returns to its equilibrium position when x = 0. 
This occurs when

That is,


Because the weight returns to the equilibrium position when t =  3 s, therefore
T = 12 s
The motion is


When t = 1 s, the position of the weight from equilibrium is