A block attached to an ideal horizontal spring executes simple harmonic motion (SHM) on a friction-less surface with amplitude A, mass m and force constant k. Answer the following questions.
(a) State the mathematical form of the total mechanical energy of this oscillator, clearly naming the physical quantities on which it depends.
(b) Explain, without detailed calculation, how the total mechanical energy will change if the amplitude of oscillation is doubled while m and k remain unchanged.
(c) Give a reasoned argument to state whether the total mechanical energy of the oscillator depends on the mass of the block when the amplitude is kept fixed.