Final answer:
To find the displacement of a weight on a spring over time, one should use the formulas related to Simple Harmonic Motion and Hooke's Law, and apply the given initial conditions to the general SHM equation.
Step-by-step explanation:
The student's question involves finding the displacement of a weight attached to a spring over time, following the principles of Simple Harmonic Motion (SHM). Given that a weight stretches the spring by 1.5 inches in equilibrium, a displacement of 8 inches from this point, and an initial velocity of 4 ft/s downwards, the student is seeking the displacement equation for t > 0. This scenario assumes that the weight encounters no resistive forces, such as friction or air resistance, and oscillates about the equilibrium position according to Hooke's Law and SHM.
To solve this problem in physics, formulas for SHM involving Hooke's Law which states F = -kx, and Newton's second law of motion will be used. Here, k is the spring constant, and x is the displacement from the equilibrium position. The motion can also be described by equations involving amplitude, angular frequency, and phase constants in the form y(t) = Acos(ωt + φ), where A is the amplitude, ω is the angular frequency, and φ is the phase constant. To find the specific solution for this question, initial conditions, such as initial displacement and velocity, should be applied to the general solution.