A linear motion stage ? moves on a machine frame. The maximum acceleration of the stage is =10 m/s2 , and the maximum allowed position error of the stage is ?=5 m. 1a) What is the required minimum natural frequency ?? of the stage? 1b) How to improve the motion stage design to reduce position error of the stage? Please suggest two ways and explain why. 1c) Suppose the stage mass ?=8 kg. Draw the Bode plot to show the magnitude and phase of the frequency response function (FRF) of this single mass system for frequency range ?=1 1000 Hz. You may draw the plot in Excel / Matlab / 20-sim, or you may draw it by hand