A body of mass m executes oscillations on a horizontal frictionless surface attached to a light spring of force constant k.
(i) Write expressions for the following physical quantities in terms of amplitude A, angular frequency ω and (where appropriate) k or m:
(a) the maximum speed,
(b) the maximum acceleration,
(c) the total mechanical energy of the system.
(ii) The amplitude of the motion is suddenly doubled while m and k remain unchanged. By what factor will each of the three quantities listed in part (i) change? Give mathematical reasoning for every answer.