Problem 10.3 = Derive the equations of motion for the system shown below if the coordinates are the position of the cart and the angle of the pendulum. The pendulum rod is massless. Assume small angular displacements. The values are: m = 20 kg, m₁ = 5 kg, l = 0.5 m, k = 30 Nm/rad, c = 10 Nm.s/rad, k = 200 N/m, cc 30 N.s/m. Hint: To sum moments about an arbitrary point P, use rp-G X (mxG + IGÖ) = ΣMp where TP-G is the position vector from point P to the center of mass G, m is the mass of the object, IG is the inertia about the center of mass, G is the acceleration of the center of mass, and Ä is angular acceleration. kc Mass mc Hinge k,c CC Moment M Gravity Force F Mass mp Find the natural frequencies and mode shapes of the system 1 Answer: w₁ = 2.77 rad/s, w₂ = 7.54 rad/s, v₁ = [0.43mad], º2 = [−8.59 rad]