Maximum acceleration in simple harmonic motion occurs at the points of maximum displacement from the equilibrium. At these points, the spring is either most compressed or most stretched.
The formula used to find maximum acceleration, , is: where is the spring constant, is the mass of the block, and is the amplitude.
This formula tells us that the greater the spring constant and the displacement (amplitude combined), the higher the acceleration:
- means stiffness increases acceleration.
- means greater displacement increases acceleration.
Acceleration reaches its peak because the spring force is greatest when displacement is greatest, rapidly pulling the block back towards equilibrium.