Here's why:
* SHM Equation: The equation for acceleration in SHM is a = -ω²x, where:
* 'a' is acceleration
* 'ω' is the angular frequency (a constant for a given system)
* 'x' is the displacement from the equilibrium position.
* Maximum Displacement: At the amplitude points, the displacement (x) is at its maximum value.
* Direct Proportionality: Since acceleration is directly proportional to displacement (a ∝ x), when displacement is maximum, acceleration is also maximum.
In simpler terms: Imagine a swinging pendulum. The pendulum's speed is highest at the equilibrium position (middle) and slows down as it reaches the highest point (amplitude). At the amplitude points, the pendulum momentarily stops before reversing direction. This change in direction requires the greatest acceleration.
