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Infinite springs with force constants k,...

Infinite springs with force constants `k, 2k, 4k and 8k …………` respectively are connected in series. The effective force constant of the spring will be

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`(1)/(k_(eff)) = (1)/(k) + (1)/(2k) + (1)/(4k) + (1)/(8k) + "……….."oo`(For infinite G.P. `S = (a)/(1+r)` where `a =` First term, `r =` common ratio)
`(1)/(K_(eff)) = (1)/(k) [1+1/2+1/4+1/8+"………"] = (1)/(k)[(1)/(1+(1)/(2))] = 2/k` so `k_(eff) = k//2`
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