A particle at the end of a spring executes simple harmonic motion with a period `t_(1)` while the corresponding period for another spring is `t_(2)` if the oscillation with the two springs in series is T then

Options

A. `T = t_(1) + t_(2)`
B. `T^(2) = t_(1)^(2) + t_(2)^(2)`
C. `T^(-1) = t_(1)^(-1) + t_(2)^(-1)`
D. `T^(-2) = t_(1)^(-2) + t_(1)^(-2)`

Answer

B

Explanation

`T = 2pisqrt((m)/(k)) rArr T^(2) prop (1)/(k)`
`t_(1)^(2) prop 1/(k_(1))` & `t_(2^(2)) prop (1)/(k_(2)) rArr t_(1)^(2) prop (1)/(k_(1)) + (1)/(k_(2))`
But `(1)/(k_(1)) + (1)/(k_(2)) = (1)/(k) prop T^(2) rArr t_(1^(2)) + t_(2^(2)) = T^(2)`