When a body is suspended from two light springs separately, the periods of vertical oscillations are `T_1` and `T_2`. When the same body is suspended from the two spring connected in series, the period will be

Options

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

Answer

D

Explanation

`T=2pisqrt(m/k)impliesTprop(1)/(sqrtk)implieskprop1/T^2`
`k_1porp1/T_1^2`, `k_2prop1/T_2^2`, `k_(eq)prop1/T^2`
`1/k_(eq)=(1)/(k_1)+(1)/(k_2)`
`T^2=T_1^2+T_2^2impliesT=sqrt(T_1^2+T_2^2)`