Problem 1. A rotor consists of a bar of Young's modulus E, density p, length L and square cross-section of side t. The rotor is spinning in the x-y plane with angular velocity about the z-axis as shown. A rigid counterweight M (= 0.1 x the mass of the bar) is attached at the bar's end (its center is at the tip of the bar). Z L M X Given for numerical calculations: E=70 GPa, p = 2700 kg/m, L=1 m, t=1 cm, c=1000 rad/s. Neglect gravitational effects. 1. Write down the potential energy of the system. Use a cubic polynomial to describe the displacement: u = a+bx+cx+dx. Solve for the coefficients a, b, c and d using the Rayleigh-Ritz (RR) method.