Given \(N=1000 lb, E=30x10^{6} psi, \upsilon=0.3, L=4 ft, \gamma=0.283 lb/in^{3}\) and a 4"x4" hollow square tube beam cross section with a wall thickness of 0.25" :
A) Derive the frequency equation for the beam.
B) Solve the frequency equation for the lowest natural frequency.
C) Show that the frequency in B is lower than the case where there is no axial load.