A block of mass m attached to a spring of force constant k oscillates horizontally with initial amplitude A on a surface offering negligible friction. After a long interval a gentle uniform resistive force causes the amplitude to drop to A/2, while m and k remain unchanged.
(i) Determine the percentage decrease in the maximum speed of the block.
(ii) Determine the percentage decrease in the maximum acceleration of the block.
(iii) Determine the percentage decrease in the total mechanical energy of the system.
(iv) Based on your results, identify which of the three quantities—maximum speed, maximum acceleration, or total energy—is most sensitive to a change in amplitude, and justify your answer mathematically.