Determine the characteristic equation by using the

Question

A uniform rod hangs freely from a hinge at the top. Using the three modes Φ₁ =x/l, Φ₂ =sin(Πx/l), and Φ₃ =(2Πx/l) ,

determine the characteristic equation by using the Rayleigh-Ritz method.

The response must be typed, single spaced, must be in times new roman font (size 12) and must follow the APA format.