From the given figure find the frequency of oscillation of the mass m

Options

A. `n=(1)/(2pi)sqrt((K)/(m))`
B. `n=(1)/(2pi)sqrt((K^(2))/(2m))`
C. `n=2pisqrt((m)/(2K))`
D. `n=(1)/(2n)sqrt((K)/(2m))`

Answer

A

Explanation

If we pull mass m towards right by a distance x then the restoring force it experiences is
F=-kx
`implies m(d^(2)x)/(dt^(2))=-kx`
`implies (d^(2)x)/(dt^(2))+(k)/(m)x=0implies (d^(2)x)/(dt^(2))+omega^(2)x=0`
where `omega=sqrt((x)/(m))`
`implies (2pi)/(T)=sqrt((x)/(m))`
`implies n=(1)/(2pi)sqrt((x)/(m))`