Two identical springs of constant ' K ' are connected in series and parallel in shown in figure. A mass ' M ' is suspended from them. The ratio of their frequencies is series to parallel combination will be

Step-by-step solution

In series combination, the effective spring constant k ₁= k 2 In the parallel combination, the effective spring constant is k ₂=2 k aligned & f ₁= 1 2 k ₁ ~m = 1 2 k 2 ~m & f ₂= 1 2 k ₂ ~m = 1 2 2 k m & f ₁ f ₂ = 1 4 = 1 2 aligned