In simple harmonic motion (SHM), the acceleration of the oscillating object is maximum at the extreme positions, specifically at the points of maximum displacement from the equilibrium position. These points are also known as the amplitude of the motion.
In SHM, the restoring force acting on the object is directly proportional to its displacement but in the opposite direction, according to Hooke's Law. The acceleration of the object is given by the equation:
a = -ω^2x
Where: a = acceleration ω = angular frequency of the motion x = displacement from the equilibrium position
In this equation, the negative sign indicates that the acceleration is opposite to the displacement, acting towards the equilibrium position.
When the object reaches the extreme positions (maximum displacement), the magnitude of the displacement (|x|) is at its highest value. Therefore, the term ω^2x in the acceleration equation is also at its maximum. As a result, the acceleration of the object is maximum at the extreme positions of the simple harmonic motion.