Two separate horizontal mass–spring systems are arranged on identical smooth tables. System A consists of a spring of constant k1=200Nm−1 carrying a mass m1=1.0kg. System B uses a different spring of constant k2=50Nm−1 and a mass m2 that can be varied.
(i) Calculate the time period of small oscillations of System A.
(ii) For System B to have the same time period as System A, determine the value of m2.
(iii) If both systems are now given the same mass of 1.0kg each, compare their frequencies of oscillation and state which system oscillates faster, giving a numerical ratio of the two frequencies.