A block of mass m is attached to a horizontal ideal spring on a friction-free table. After being pulled from equilibrium and released, the block undergoes simple harmonic motion with an initial amplitude A. No numerical values for m, k, or A are provided; you may symbolize any needed quantities.
Answer the following questions qualitatively and algebraically where appropriate.
(1) Part 1: (a) Describe, in words and with an algebraic relationship, how the total mechanical energy of the block–spring system depends on the amplitude of oscillation when the spring constant remains unchanged.
(2) Part 2: (b) The block is pulled so that its new amplitude is 2A and released from rest. Explain how the maximum kinetic energy in this second motion compares with the maximum kinetic energy in the original motion, and justify your reasoning without performing a full numeric calculation.
(3) Part 3: (c) Over many cycles a very small non-conservative force slowly reduces the amplitude to A/2. Sketch or verbally describe the qualitative changes you would expect to see in graphs of (i) kinetic energy versus time and (ii) potential energy versus time over several oscillations as the amplitude decreases. Focus on how the peak values and general shape evolve.