Final answer:
The displacement of an oscillator with no initial velocity and starting at maximum amplitude A is described by the equation x(t) = A × cos(ωt), with ω being the angular frequency.
Step-by-step explanation:
The formula for the displacement x(t) of an oscillator starting at maximum amplitude x = A and with no initial velocity is given by the equation:
x(t) = A × cos(ωt), where ω is the angular frequency.
At time t = 0, the initial displacement x0 equals the amplitude A. The oscillator then moves back and forth with a period T, returning to x = A when t = T because cos(2π) = 1. This differs from the kinematic equation x = x0 + v0t + ½at², which is typically used for linear motion with constant acceleration, not oscillatory motion.