The frequency of vibration f of a mass m suspended from a spring of spring constant k is given by a relation f=cm^xk^y; where c is a dimensionless quantity. The value of x and y are

Given relation

f = cm^xk^y

where f = Frequency of vibration

       m = Mass suspended from a spring

        k = Spring constant

        c = Dimensionless quantity 

By putting the dimensions of each quantity on both the sides, we get

[T⁻¹ ] = [M]^x [MT⁻² ] ^y

 

On comparing the dimensions of quantities on both sides, we get

x + y = 0 and 2y = 1

 

→ y = 1/2

 

and x = −1/2