The frequency f of vibration of mass m suspended from a spring of spring contact k is given by f=c mx ky. Where c= dimensionless constant, then find the values of x and y.
In this situation dimension of RHS=LHS
i.e, [f]=[cmxky]
[T−1]=[Mx][MyT−2y]=[Mx+yT−2y], since [k]=[MT−2]
comparing both sides we get,
x+y=0,and−1=−2y⇒y=1/2
and x=−y=−1/2