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-L₁0)+ k₂ (x + L20)=0 JÖ-k₁₁ (x-1)+ k₂ L₂ (x+120)=0 W W=3220 lb L₁ = 4.5 ft; k₁ =2400 lb/ft; Je ミード 2-mr2 g L2=5.5 ft k2=2600 lb/ft; r=4 ft; g=32.20 ft/s²