The frequency of oscillation of the spring shown in the figure will be

Options

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

Answer

D

Explanation

As spring are connected in series , effective force constant
`(1)/(k) = (1)/(k_(1)) + (1)/(k_(2)) rArr k = (k_(1)k_(2))/(k_(1) + k_(2))`
Hence frequency of oscillation is
`n = (1)/(2pi) sqrt((k)/(m)) = (1)/(2pi) sqrt((k_(1)k_(2))/((k_(1) + k_(2)) m))`