The correct answer is option 3: The acceleration of a particle executing simple harmonic motion is minimum when the speed is maximum.

Let`s dissect each option to better understand why option 3 is correct:

Option 1: It states that the acceleration is always in the opposite direction to velocity. This is not true for simple harmonic motion. In simple harmonic motion, the acceleration is directed towards the equilibrium position, while the velocity is maximum at the equilibrium position and changes direction at the extremities.

Option 2: It states that the acceleration is proportional to the frequency of oscillation. This is also not true for simple harmonic motion. The acceleration of a particle in simple harmonic motion depends on the displacement from the equilibrium position, not the frequency.

Option 3: This is the correct answer. In simple harmonic motion, the speed of the particle is maximum at the equilibrium position and decreases as the particle moves away from it. At the extremities, when the speed is minimum, the acceleration is maximum. Therefore, the acceleration is minimum when the speed is maximum.

Option 4: It states that the acceleration decreases as the potential energy increases. This is not true for simple harmonic motion. The potential energy increases as the particle moves away from the equilibrium position, but the acceleration is