Two spring of force constants k and 2k are connected to a mass as shown in figure. The frequency of oscillation of the mass is……..

Options

A. `(1)/(2pi) sqrt((k)/(m))`
B. `(1)/(2pi) sqrt((2k)/(m))`
C. `(1)/(2pi) sqrt((3k)/(m))`
D. `(1)/(2pi) sqrt((m)/(k))`

Answer

C

Explanation

`F_(1)= k_(1)Y" and "F_(2)= k_(2)Y`
`therefore F= F_(1)+F_(2)= (k_(1)+k_(2))Y`
`therefore k= k_(1)+ k_(2)`
`f= (1)/(2pi) sqrt((k)/(m))= (1)/(2pi) sqrt((k_(1)_k_(2))/(m))`
`therefore k_(1)= k, k_(2)= 2k`
`therefore f= (1)/(2pi) sqrt((3k)/(m))`.