Problem 2 Two carts of mass m each are connected by a spring and move on a horizontal smooth surface in a straight line, as shown in Figure 1. SAD x40 Figure 1: Two connected carts move on a horizontal smooth surface in straight line. 1 1. Derive equations of motion and write them in matrix form. 2. Determine the natural frequencies when c = 0, and mode shapes (eigen-vectors) of oscilla- tion of the system. 3. Explain the physical meaning of the zero natural frequency response. 4. Find modal equations for the modal coordinates when the damping exists. Are they decou- pled?