Consider a system with three mass connected to four springs, shown in Figure 3. (a) Derive the set of differential equations that describes their motion in time. Write the three different equations in matrix form, [acceleration vector] + [k/m matrix][displacement vector] = 0) (7) Note each equation has been divided by the mass. (b) Solve for the eigenvalues and natural frequencies for the following values of mass and spring constants: ki = k4 = 15 N/m, k2 = k3 = 35 N/m, and m = m2 = m3 = 1.5 kg. - X1 X2 * ka Consider a system with three mass connected to four springs, shown in Figure 3. (a) Derive the set of differential equations that describes their motion in time. Write the three different equations in matrix form, [acceleration vector] + [k/m matrix][displacement vector] = 0) (7) Note each equation has been divided by the mass. (b) Solve for the eigenvalues and natural frequencies for the following values of mass and spring constants: ki = k4 = 15 N/m, k2 = k3 = 35 N/m, and m = m2 = m3 = 1.5 kg. - X1 X2 * ka