Springs of constants K, 2K, 4K, 8K, 16K,… are connected in series. The mass ‘m’ kg is attached to the lower end of the last spring and the system is allowed to vibrate. The frequency of oscillation is

K, 2K, 4K, 8K, 16K,… are connected in series1Keffective=1K+12K+14K+−−→−geometric progression(gp)  sum to infinite series of gp =a1-r; a is first term; r is common ratio 1Keff=1K1+12+122+...  here first term a=1 and common ratio r=12    1Keff=1Ka1-r  substitute the values 1Keff=1K11-12 1Keff=1K21Keff=K2 Frequency n=12πKeffm  ; substitute obtained value of Keff n=12πK2mn=12πK2m