Two spring of force constants `K` and `2K` are connected a mass `m` below The frequency of oscillation 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

`n = (1)/(2pi) sqrt((k_(effective))/(m))`
spring are connected in parallel
`k_(eff) = k_(1) + k_(2)= k + 2k= 3k`
`rArr n = (1)/(2pi) sqrt(((k + 2k))/(m)) = (1)/(2pi) sqrt((3k)/(m))`