A particle at the end of a spring executes S.H,M with a period `t_(2)` If the period of oscillation with two spring in .

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_(2)^(-2)`

Answer

B

Explanation

`t_(1) = 2pi sqrt((m)/(k_(1))) and t_(2) 2 pi sqrt((m)/(k_(2)))`
in series effective spring constant `k = (k_(1)k_(2))/(k_(1) +k_(2))`
`:. Time period T = 2pi sqrt((m(k_(1) + k_(2)))/(k_(1)k_(2)))`…..(i)
Now `t_(1)^(2) + t_(2)^(2)= 4pi^(2)m((1)/(k_(1)) + (1)/k_(2)) = (4pi^(2)m(k_(1) + k_(2)))/(k_(1)k_(2))`
`t_(1)^(2) + t_(2)^(2)= T^(2)`. [Using equation (ii)]