A block of mass is connected to an ideal spring of stiffness `K_(1)` on left hand side and to an elastic strig of stiffness `K_(2)` on right hand side as shown in figure the time period of motion if mass m is displaced by 'x' as shown in figure.

Options

A. `2pisqrt(m//K_(1))`
B. `2pisqrt(m//(K_(1)+K_(2)))`
C. `2pisqrt(m(K_(1)+K_(2))//K_(1)K_(2))`
D. `pi(sqrt((m)/(K_(1)+K_(2)))+sqrt((m)/(K_(1))))`

Answer

D

Explanation

`T=(T_("left"))/(2)+(T_("right"))/(2)=pisqrt((m)/(K_(1)+K_(2)))+pisqrt((m)/(K_(1)))`
Note string becomes slack when mass pushes te string.