A rectangular RCC machine foundation of size 3.0 x 3.0 x 0.8m thick is supporting a machine of weight is 10kN. The machine transmits an unbalanced vertical load passing through the combined CG of the machine and foundation whose amplitude is 8[1-sin/4t]kN Soil medium has the following properties: Young’s modulus, E=1.2 x105 kN/m2 . Poisson’s ratio, v=0.3. Unit weight of soil and concrete, s=17 kN/m3 . c=17 kN/m3 Find the response of the system and natural frequency using Elastic half- space approach for vertical and sliding vibration