see picture
part d
write in the form and identify the amplitude, angular frequency, and the phase shift of the spring motion. record your answers in the response box.
part e
the angle represents the phase shift, determined by the initial conditions of the experiment or the position of the weight at t = 0. if the weight is at its maximum positive position (weight is above equilibrium) at t = 0, then = 0. if the weight is at its maximum negative position (spring is stretched and weight is below equilibrium) at t = 0, then . if the weight is traveling in the negative direction and passing through equilibrium at t = 0, then . in the response box, describe the initial condition of our experiment; specifically, describe the position of the weight and the direction in which it was traveling.
part f
find the times (to the nearest hundredth of a second) that the weight is halfway to its maximum negative position over the interval . solve algebraically, and show your work and final answer in the response box. hint: use the amplitude to determine what y(t) must be when the weight is halfway to its maximum negative position. graph the equation and explain how it confirms your solution(s).