Two spring are connected toa block of mass `M` placed a frictionless surface as shown if both the spring have a spring constant `k` the frequency of oscillation block is

Options

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

Answer

C

Explanation

In this case the two springs are connected in series and the spring constant K' is given by
`K' =(K_(1)+K_(2))/(K_(1)+K_(2))=(K^(2))/(2K)=(K)/(2) (because K_(1)=K_(2))`
`therefore " The frequency " (v) =(1)/(2pi ) sqrt((K')/(m))=(1)/(2pi) sqrt((K)/(2m))`