Two weightless springs have force constants `k_(1)` and `k_(2)` and connected in series. The combination is loaded with m, the time period of oscillation is :

Options

A. `T=2pi sqrt((m)/(k_(1)+k_(2)))`
B. `T=2pi sqrt(m((1)/(k_(1))+(1)/(k_(2))))`
C. `T=2pi sqrt(("m k"_(1)k_(2))/(k_(1)+k_(2)))`
D. none of these.

Answer

B

Explanation

In series `(1)/(k_(s))=(1)/(k_(1))+(1)/(k_(2))`
`implies" "T=2pi sqrt((m)/(k_(s)))`
`T=2pi sqrt(m((1)/(k_(1))+(1)/(k_(2))))`
So the correct choice is (b).