Consider the following statements : A simple pendulum is set into oscillation. Then I. the acceleration is zero when the bob passes through the mean position. II. in each cycle the bob attains a given velocity twice. III. both acceleration and velocity of the bob are zero when it reaches its extreme position during its oscillation. IV. the amplitude of oscillation of the simple pendulum decreases with time. Which of these statements are correct ?

Statements I and II are correct while III and IV are incorrect. For a simple pendulum executing (ideal) simple harmonic motion, acceleration is proportional to displacement and directed opposite to it (a = −ω^2 x), so at the mean position (x = 0) acceleration is zero while velocity is maximum, supporting I and the fact that each nonzero speed value (magnitude) is achieved twice per cycle (once in each direction) supports II. At the extreme positions the velocity is zero but acceleration is maximum (not zero), so III is false. In ideal SHM (no damping) the amplitude remains constant; amplitude only decays with time if dissipative (damping) forces act, so IV is false for an ideal simple pendulum.