A massless Rod AB is hinged at point A. At point P, it is connected by a spring of stiffness `K_(1)` and at point B it is connected to another spring of stiffness `K_(2)` connected to mass m as shown in figure the length of Rod AB is l and displaced by a distance x from its mean position as shown in figure then the time period of S.H.M. of mass is

Options

A. `2pisqrt((m(K_(2)b^(2)+K_(1)L^(2)))/(K_(1)K_(2)b^(2)))`
B. `2pisqrt((m(K_(2)L^(2)+K_(1)b^(2)))/(K_(1)K_(2)b^(2)))`
C. `2pisqrt((m(K_(1)K_(2)b^(2)))/(K_(2)b^(2)+K_(1)L^(2)))`
D. `2pisqrt((m(K_(2)L^(2)+K_(1)b^(2)))/(K_(2)b^(2)))`

Answer

B

Explanation

`(X_(2))/(b)=(X_(1))/(l)to(1)`
torque equation about Hinge
`K_(2)(x-x_(1)).l=K_(1)x_(2).bto(2)`
Substituting `X_(2)` from equation (1) & on solving we get
`X_(1)=(K_(2)L^(2)x)/([K_(2)L^(2)+K_(1)b^(2)])`
Equation of mass `F=ma=-K_(2)(x-x_(1))`
On solving `=a=(-K_(1)K_(2)b^(2)x^(2))/(m(K_(2)L^(2)+K_(1)b^(2)))`