1. From a simplified simulation for an automobile suspension system the equations of motion are found below. With the following given data. Determine: (a) determine the two natural frequencies of the system, (b) determine the two normal modes of the system, (c) write-out the normal modal matrix [P]. (d) diagonalize the stiffness matrix using the normal modal matrix [P], (e) diagonalize the mass matrix using the normal modal matrix [P], (f) express the orthonormal modal matrix [P] mx+k₁ (x-L)+ k₂ (x + L20)=0 JÖ-k₁₁(x-1)+ k₂ 12 (x + L20)=0 W=3220 lb L₁-4.5 ft k₁-2400 lb/ft: Je= W 8 L2-5.5 ft k2=2600 lb/ft; -4 f g = 32.20 ft/s² mr