Final Answer:
The equilibrium position in simple harmonic motion is the position of zero displacement and maximum velocity. Thus option d is correct.
Step-by-step explanation:
In simple harmonic motion (SHM), an oscillating system moves back and forth around a central point. The equilibrium position is where the object experiences zero displacement and maximum velocity. At this point, the restoring force is at its minimum, causing the object to neither move towards nor away from the mean position. In SHM, the equilibrium position signifies the stable state where the object's displacement is zero, and its velocity is at its maximum.
During SHM, the displacement from the equilibrium position, denoted as x, oscillates sinusoidally. At the equilibrium position, x = 0, indicating zero displacement. However, the velocity, v, is maximum at this point, as the restoring force has brought the object to its farthest point from the mean position. The velocity is given by v = ωA, where ω represents the angular frequency of oscillation and A is the amplitude of the motion. As x = 0, the kinetic energy is maximum while the potential energy is minimum at this position, as all the energy is kinetic.
Understanding the equilibrium position in SHM is crucial as it marks the stable point where the object's displacement is zero, and its velocity is at its maximum. This point signifies the balance between potential and kinetic energy, forming the basis of understanding oscillatory motion in various physical systems.
Thus option d is correct.