The spring as shown in figure is kept in a stretched position with extension `x` when the system is relesed. Assuming the horizontal surface to be frictionless, the frequency of oscillation is

Explanation

There is no external force on the system hence centre of mass remains at rest.
Let `m_1` moves towards left by `x` and `m_2` moves towards right `x^'`.
`x+x^'=x_0` (i)
`m_1x=m_2x^'` (ii)
Solving `x=(m_2x_0)/(m_1+m_2)`, `x^'=(m_1x_0)/(m_1+m_2)`
Tension in the spring
`T=kx_0=(k(m_1+m_2))/(m_2)x`
Restoring force `F=-(k(m_1+m_2))/(m_2)x`
`a=F/m_1=-(k(m_1+m_2))/(m_2)x=-omega^2x`
`T=2pisqrt((m_1m_2)/((m_1+m_2)k)`
`f=1/T=(1)/(2pi)sqrt((k(m_1+m_2))/(m_1m_2))`