f=amxky ....(i) Dimensions of frequency v=[M0L0T−1] Dimensions of constant a=[M0L0T0] Dimensions of mass m=[M] Dimensions of spring constant k=[MT−2] Putting these value in equation (i), we get [M0L0T−1]=[M]x[MT−2]y Applying principle of homogeneity of dimensions, we get x+y=0 −2y=−1 or x=−