Here we look at the modal frequencies for the Ritz Method Example for a beam in bending with clamped-free boundary conditions, and a tip mass μmℓ at the free end. The method for solving this problem is given in the Ritz Method Example.

This short demo lets you see how the modal frequencies are affected by changing various parameters. As you increase the number of mode shapes, you see higher frequency terms appear. Additionally, you can see that the lower order modes approach their exact values.

Finally, try varying the mass of the tip mass and beam to see how this affects the frequencies. Does this make sense, intuitively?