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? a. d=-9cos(pi/3)t b. d=-9cos(2pi/3)t c. d=-3cos(pi/9)t d. d=-3cos(2pi/9)t

For a better understanding of the explanation provided here kindly go through the file attached.

Since, the weight attached is already at the lowest point at time, t=0, therefore, the equation will have a -9 as it's "amplitude" and it will be a Cosine function. This is because in cosine function, the function has the value of the amplitude at t=0.

Now, we know that the total angle in radians covered by a cosine in a given period is and the period given in the question is t=3 seconds. Therefore, the angular velocity, of the mentioned system will be:

Combining all the above information, we see that the equation which models the distance, d, of the weight from its equilibrium after t seconds will be:

Thus, Option B is the correct option. The attached diagram is the graph of the option B and we can see clearly that at t=3, the weight indeed returns to it's original position.

c. (3,2,6) is the answer.