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. (a) `T^(-1)=t_(1)^(1)+t_(2)^(-1)`
B. (b) `T^(2)=t_(1)^(2)+t_(2)^(2)`
C. (c )`T=t_(1)+t_(2)`
D. (d) `T^(-2)=t_(1)^(-2)+t_(2_^(2)`

Answer

B

Explanation

(b) For first spring, t_(1)=2pisqrtm/k_(1)`,
For second spring, `t_(2)=2pisqrtmk_(2)`.
when springs are in series then, `(k_(1)k_(2))/(k_(1)k_(2)`
:. `T=2pisqrt((m(k_(1)+k_(2))))/((k_(1)k_(2)`.
:. `T=2pisqrtm/k_(2)+m/k_(1) =2pisqrt((t_(2)^(2))/(2pi^(2)+t_(1)^(2)/(2pi)^(2))`
`rArr T^(2)=t(1)^(2)+t_(1)^(2)`.
where x is the displacement from the mean position.