A particle attached to an ideal horizontal spring executes simple harmonic motion described by x(t)=Acos(ωt+ϕ), where the usual symbols have their standard meanings.
(i) Write the expressions for the instantaneous velocity v(t) and acceleration a(t) in terms of A,ω, and ϕ. Do not perform any differentiation in your answer.
(ii) At a certain instant the displacement of the particle is positive and its magnitude is decreasing. State the sign of the velocity at that instant and justify your answer.
(iii) If, at the same instant, the acceleration of the particle is negative, deduce the possible range of the phase angle (ωt+ϕ) expressed in radians. Explain your reasoning briefly.