Q.4. A cantilever beam of length 1 m with two masses 2 kg each, one at the end and the other at the middle is subjected to a vertical force of 5 sint N at the middle. Derive the equation of motion using flexibility matrix method. Find the natural frequency and mode shapes of the system. Use normal mode summation method i.e. using single mode approximation find the forced response of the system. Also show how this response differs when you consider all the modes participate in the resulting oscillation. E = 200GN/m². Consider rectangular cross-section of the shaft with width 10mm and thickness 5mm.