A bead of mass m is attached to the mid-point of a taut, weightless string of length and placed on a frictionless horizontal table. Under a small trverse displacement x , as shown, if the tension in the string is T , then the frequency of oscillation is-

Step-by-step solution

Let the angle of T with the vertical be then F.B.D. 2 ~T = ma also = x x²+ ( 2 )² given >>x ² 4 +x² ² 4 a = -2 Tx m ( 2 ) (negative sign for restoring force) or a =- ( 4 ~T ~m ) x also this is similar to the equation of SHM i.e. a =- ² x array l = 4 T m & f= 2 f= 1 2 4 T m array