Two springs are made to oscillate simple harmonically due to the same mass individually. The time periods obtained are `T_1` and `T_2`. If both the springs are connected in series and hten made to oscillate by the same mass, the resulting time period will be

Options

A. `T_1+T_2`
B. `(T_1T_2)/(T_1+T_2)`
C. `sqrt(T_1^2+T_2^2)`
D. `(T_1+T_2)/(2)`

Answer

C

Explanation

Let spring constant of two spring are `k_1` and `k_2` respectively then
`T_1=2pisqrt((m)/(k_1))` and `T_2=2pisqrt((m)/(k_2))`
`k_1=(4pi^2m)/(T_1^2)` and `k_2=(4pi^2m)/(T_2^2)`
When the two springs are connected in series then
`T=2pisqrt((m)/(k_(eq)))` where `k_(eq)=(k_1k_2)/(k_1+k_2)`
`T=sqrt(T_1^2+T_2^2)`