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.

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Infinity Learn · Accepted Answer

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 $$T=2$$$$π$$$$mkeff=2$$$$π$$$$mk/2=2$$$$π$$$$2mk$$

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.

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