A particle is executing simple harmonic motion. Which one of the following statements about the acceleration of the oscillating panicle is true ?

In simple harmonic motion (SHM), the acceleration of a particle is defined by the relationship a = -ω²x, where 'x' is the displacement from the equilibrium position [2]. This means acceleration is directly proportional to displacement but acts in the opposite direction [1]. At the equilibrium position (x = 0), the acceleration is zero (minimum) [2]. Conversely, the velocity of the particle is at its maximum when it passes through this equilibrium position [2]. Therefore, acceleration is minimum when the speed is maximum. Statement 1 is false because acceleration and velocity are in the same direction when the particle moves toward equilibrium [2]. Statement 2 is incorrect as acceleration is proportional to the square of the frequency (a ∝ f²) [2]. Statement 4 is false because potential energy is maximum at extreme displacements where acceleration is also at its maximum magnitude [2].

Sources

1. [1] https://www.sciencedirect.com/topics/engineering/simple-harmonic-motion
2. [2] https://www.birmingham.ac.uk/study/undergraduate/schools-and-colleges/post-16/a-level-stem-resources/simple-harmonic-motion