A 3-DOF system has the following properties: m = 8.0 kip-s/in m2 = 6.0 kip-s/in m3 = 4.0 kip-s/in k - 250 kip/in k = 220 kip/in k3= 170 kip/in m m m Rigid beams k 2 k Determine all three modal natural frequencies and the associated mode shapes. Perform this calculation by hand, developing the cubic characteristic equation and finding its roots. It can be very helpful to plot the equation in Excel and seek each root visually, then using the Solver to determine the precise value for each root.