Two identical springs of constant ' k ' are connected in series and then in parallel. A mass ' m ' is suspended from them, the ratio of their frequencies of vertical oscillations will be

Step-by-step solution

The effective spring constant for two identical springs in series is k_s = k 2 , while for parallel connections it is k_p = 2k . The frequency of vertical oscillations for a mass m is given by f = 1 2 k_ eff m , so f_s = 1 2 k 2m and f_p = 1 2 2k m . The ratio is f_s f_p = k/2m 2k/m = 1 4 = 1 2 , giving the frequency ratio 1:2 . The final answer is D