Final answer:
The position of an oscillator at maximum displacement is at the amplitude (A), where the object has the maximum potential energy in simple harmonic motion.
Step-by-step explanation:
The position of an oscillator when starting from maximum displacement is at the point where the object has been pulled or pushed the farthest from its equilibrium position, typically referred to as amplitude (A). In simple harmonic motion (SHM), this position is where the object holds the maximum potential energy. As the object is released, it will accelerate toward the equilibrium position, indicated as x = 0, which is the point where the spring is neither stretched nor compressed.
Imagine we have an object attached to a spring on a frictionless surface. When the object is displaced to x = A and let go, it starts to move towards the equilibrium with increasing speed, reaching maximum velocity at x = 0. The motion continues past the equilibrium due to inertia until the spring is fully compressed and the object reaches a displacement of x = -A on the opposite side. The object then reverses direction, accelerating back towards x = 0 and continues the cycle. The spring’s stiffness and the mass of the object determine the oscillation's period (T), with a stiffer spring resulting in a shorter period and a larger mass leading to a longer period.