Simple Harmonic Motion — Acceleration at Mean Position For a particle in SHM, what is the magnitude of acceleration at the mean (equilibrium) position?

Introduction / Context:
In simple harmonic motion (SHM), displacement, velocity, and acceleration vary sinusoidally with time. Understanding where each quantity is maximum or zero is key to sketching motion and solving related dynamics problems.

Given Data / Assumptions:

• Standard SHM: x(t) = A sin(ω t + φ).
• Mean position corresponds to x = 0 (equilibrium).

Concept / Approach:
Acceleration in SHM is proportional to displacement and directed toward the mean position: a = -ω^2 x. Therefore, acceleration depends directly on x, not on velocity. At x = 0, a must be zero.

Step-by-Step Solution:

Verification / Alternative check:
Velocity at mean position is maximum (energy is all kinetic), which coexists with zero acceleration because the slope of velocity (change rate) crosses zero at the instant of peak speed in sinusoidal motion.

Why Other Options Are Wrong:
'Maximum' acceleration occurs at extreme displacements x = ±A; 'minimum' is ambiguous but not appropriate here because acceleration actually becomes zero at the mean, not a small positive minimum.

Common Pitfalls:
Mixing up where velocity and acceleration are maximum; thinking acceleration must be large when the speed is large—this is not true for SHM at the instant of passing equilibrium.

Final Answer:
zero.