A particle at the end of a spring executes S.H,M with a period `t_(1)`while the corresponding period for another spring is `t_(2)` . If the period of oscillation with two spring in series is T then

Options

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

Answer

B

Explanation

`T_(1) = 2pi sqrt((m)/(k_(1))) , T_(2) = 2pi sqrt((m)/(k_(2))) , T = 2pi sqrt((m)/(k_(eq)))`
`K_(eq) = (K_(1)K_(2))/(K_(1)+K_(2))` (for series), `t_(1)^(2) = (2pi m)/(K_(1))`
`t_(2)^(2) =(2pi m)/(K_(2))` and `T^(2) = 2pi m ((1)/(k_(1)) + (1)/(k_(2)))`
`rArr T^(2) = t_(1)^(2) + t_(2)^(2)`