The frequency of vibration f of a mass m suspended from a spring of spring constant K is given by a relation of this type f =CmxKy; where C is a dimensionless quantity. The value of x and y are
By putting the dimensions of each quantity both sides we get [T−1]=[M]x[MT−2]y
Now comparing the dimenstions of quantities in both sides we get x+y =0 and 2y =1
∴ x = - 12, y = 12