Springs of force 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

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Infinity Learn · Accepted Answer

K, $$2K$$, $$4K$$, $$8K$$, $$16K$$,… are connected in serieseffective spring constant is $$Keffective=Keff$$ $$is1Keff=1K+12K+14K+$$−−−$$1Keff=1K1+12+122+$$... , the paranthesis part is in geometric progression whose first term $$=1$$ and common ratio is $$r=12sum$$ to infinite terms is S∞$$=a1-r$$ where a is first term, r is common ratio  $$1Keff=1Ka1-r=1K11-121Keff=1K21Keff=K2Frequency$$   η$$=12$$$$π$$$$Keffm=12$$$$π$$$$K2m$$ due to series of springs new frequency $$is=12$$$$π$$$$K2m$$

Springs of force 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

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