The frequency f of vibrations of a mass m suspended from a spring of spring constant k is given by f=Cmxky, where C is a dimensionless constant. The values of x and y are, respectively,

force constant K=F∆xf=Cmxky. Writing dimensions on both sides,M0L0T−1=MxML0T−2y=Mx+yT−2yComparing dimensions on both sides, we have0=x+y and −1=−2y ⇒y=12,x=−12Aliter. Remembering that the frequency of oscillation of loaded spring isf=12πkm=12π(k)1/2m−1/2 which gives x=−12 and y=12