3.1. By using Newton's second law, obtain the differential equations of motion of the multi-degree of freedom system shown in Fig. P3.1." mi m2 m3 wwwww₤ wwww Fig. P3.1 3.2. By using Lagrange's equation, obtain the differential equations of motion of the system shown in Fig. P3.1. 3.3. Determine the natural frequencies and the mode shapes for Problem 3.1. assuming k₁ = k₂ = k3=k4= k 1 x 10 N/m, and m, my=m= m = 2 kg. 3.4. Repeat Problem 3.3, for the case in which k₁ = k₂ = k3=kk and my " m2 = 2m and my = m. of 3.5. Obtain the differential equations of free vibration of the three degree o freedom system shown in Fig. P3.2 by using Newton's second law. Assume small oscillations.