For a mass–spring system the time period of oscillation is T when a mass m is attached to a spring of force constant k.
Calculate the new time period in each of the following independent cases, expressing your answer in terms of T only:
(a) The mass is changed to 4m while the same spring is used.
(b) The spring is replaced by another spring of force constant 4k while the mass remains m.
(c) The mass is reduced to 2m and simultaneously the spring is replaced by one whose force constant is 4k.