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((k)/(2M))`
B. `(1)/(2pi) sqrt((k)/(M))`
C. `(1)/(2pi) sqrt((2k)/(M))`
D. `(1)/(2pi) sqrt((M)/(k))`

Answer

A

Explanation

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