Final answer:
The magnitude of the spring's displacement when the acceleration of the box is zero is equal to the amplitude of the motion in simple harmonic motion.
Step-by-step explanation:
The displacement of an object attached to a spring can be determined when the acceleration of the object is zero. In simple harmonic motion (SHM), the maximum displacement of the object from its equilibrium position is equal to the amplitude of the motion. Therefore, when the acceleration is zero, the magnitude of the spring's displacement is equal to the amplitude of the motion.
For example, in the given scenario where a 5.00-kg mass is attached to a spring with a 100 N/m spring constant, the amplitude of the motion is x = 4.00 cm. When the acceleration is zero, the magnitude of the spring's displacement is also 4.00 cm.
This situation occurs at the equilibrium position where the spring is neither stretched nor compressed. The equilibrium position is marked as x = 0, and this is where the net force on the mass is zero, which in turn means the acceleration is zero.
Therefore, when the acceleration is zero, the spring's displacement from its relaxed (equilibrium) position is also zero.