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Question

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 parts separately, then the periods are T1 & T2 then find T1/T2

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Solution

R.E.F image
F=kl
a=kml
w=km
T=2πmk
for l/4:
F=k4l
a=k4ml
w=k4ml
w=k4m
T1=2π4mk
for 3l/4:
F=3k4l
a=3k4ml
w=3k4m
T2=2π4m3k
So, T1T2=2π4mk2π4m3k
T1T2=31

1125239_1033053_ans_2b0901ee54b84faa83b63da34cd40b9e.jpg

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