A block attached to an ideal horizontal spring undergoes simple harmonic motion (SHM) along the x-axis. A verbal description of its motion during one full cycle is given below.
• At time t=0, the block is at its maximum positive displacement +A and is instantaneously at rest.
• It then moves toward the equilibrium position, crossing x=0 after some time, reaches −A, and finally returns to +A after completing one period T.
Throughout this question, assume the motion is undamped and no external forces act on the block other than the spring force.
(a) Within the interval 0<t<21T, identify all times (expressed as simple fractions of T) at which the block’s velocity is exactly zero. Describe what is happening to the block’s position at each of those instants.
(b) Still within 0<t<21T, identify the time(s) at which the block’s acceleration is exactly zero. Explain how these instants relate to both the block’s position and velocity.
(c) Consider doubling the amplitude of the oscillation to 2A while keeping the same spring and mass. Explain qualitatively whether the times you listed in parts (a) and (b) would change, and justify your answer.
(d) Using your reasoning from parts (a)–(c), explain why the quantity “period” is classified as a property of the spring–mass system rather than of the specific oscillation that happens to be set in motion.