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Q.

Consider two identical springs each of spring constant k and negligible mass compared to the mass M as shown. Fig-1 shows one of them and Fig-2 shows their series combination. The ratios of time period of oscillation of the two SHM is TbTa=x , where value of x is______. (Round off to the Nearest Integer)

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answer is 2.

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Detailed Solution

In figure (1) force constant  is  ka=k
In figure (2)  force constant is kb=k   kk+k=k2they  are  joined  in  series
Time period of spring      T=2πMK  T1k

 TbTa=kakb=kk2=2
 

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