A particle executes simple harmonic motion along the x-axis and its displacement at time t is described by x(t)=Acos(ωt+ϕ).
(i) What is meant by the “phase” of the motion? Distinguish between initial phase and phase at time t.
(ii) If, at a certain instant, the displacement is positive and its magnitude is decreasing, identify the sign (positive, negative or zero) of the velocity and of the acceleration at that instant. Give reasons for your answer.
(iii) The particle is observed at an instant when it passes through the equilibrium position heading towards the positive extreme. State the sign of the velocity and of the acceleration at that instant and justify your answer.