Obtain an equation for the frequency of oscillation of spring of force constant k to which a mass m is attached.

Explanation

Let a spring of negligible mass is suspended from a fixed point and mass m is attached as shown. It it pulled down by a small distance 'x' and allowed free it will execute simple harmonic oscillations.

Displacement from mean position = x. The restoring forces developed are opposite to displacement and proportional to `'x'.therefore F prop -x or F=-kx` where k is constant of spring. (`-ve` sign for opposite direction)
Acceleration `a=F/m=Kx/mrArrx/a=m/K`
Time period
`T=2pisqrt(("displacement")/("acceleration"))=2pisqrt(x/a)`
For spring `x/a=m/k therforeT=2pisqrt(m/K)`
`therefore` Time period of loaded spring `T-2pisqrt(m/K)`.