Springs of spring constants K,2K,4K,8K,…,many are connected in series. A mass 'm' is attached to one end. The system is allowed to oscillation. The time period is approximately.

springs are in series, whose spring constants are k,2k,4k,8k,........ effective spring constant is keffective=keff is 1keff=1k+12k+14k+... 1keff=1k1+12+122+... the brackett part is in geometric progression, infinite series, whose sum=a1-r 1keff=1ka1-r here a=1and r=12 1keff=1k11-12 1keff=1k21 keff=k2 The effective Time period of springs in series is T=2πmkeff=2πmk/2=2π2mk