A metal rod, 0.5 m long, has a rectangular cross section of
area 2 mm2.
(b) The rod is firmly clamped at the bottom as shown in the figure below,
and at the top a force F is applied in the y-direction as shown (parallel to
the edge of length b). The result is a static deflection, y, given by
y = 4F(L)^3/(Ya(b)^3)
If the force F is removed and a msss m, which is much greater than the mass
of the rod, is attached to the top en dof the rod, what is the ratio of the
frequencies of vibration in the y and x directions (i.e., parallel to the edges
of length b and a)?