4. A particular vibration absorber can be modelled as sketched in Figure below. A massive platform of mass M is mounted on a horizontally flexible foundation that exerts a horizontal restoring force Kd when the platform moves a distance d hori- zontally. Also, a mass spring system sketched in figure XX moves without friction along the horizontal surface of the platform. Derive the equation(s) of motion for the system. Begin by selecting a complete and independent set of generalized coor- dinates, starting with x1(t) and then x2(t), as necessary. Note that the meanings of these coordinates remain to be clearly defined. Answer: (Mm) + m2 + Kx mai+m2 + 2kx2 = 0 OR M+ (K+2k)x - 2kx2 = 0 mx2-2kx1 + 2kx2 = 0 = 0 K m M