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A body is in SHM with period T when oscillated from a freely suspended spring. If this spring is cut in two parts of length ratio 1 : 3 & again oscillated from the two the two parts separatedly, then the periods are T_(1) & T_(2) then find T_(1)//T_(2) .

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A block of mass m , when attached to a uniform ideal apring with force constant k and free length L executes SHM. The spring is then cut in two pieces, one with free length n L and other with free length (1 - n)L . The block is also divided in the same fraction. The smaller part of the block attached to longer part of the spring executes SHM with frequency f_(1) . The bigger part of the block attached to smaller part of the spring executes SHM with frequency f_(2) . The ratio f_(1)//f_(2) is

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