For a single degree of freedom, frequency is 3.13/sqrt deflection as you stated. That would be for example a cantilever beam with end mass only and no mass distributed weight ( that is, massless beam). In your case it is a multiple degree of freedom system with many modes, because you can think of the beam with an infinite number of masses all at different distances from the end. The first mode in this case is 3.89/sqrt deflection (NOTE I SAID 3.48/sqrt deflection befiore, sorry, use 3.89). The second mode is 24,.75/sqrt deflection, etc.