Figure 1 depicts a mechanism illustrating a statically unbalanced load mounted on the shaft of a DC motor. The DC motor is used to precisely control the angular position of the load. The task involves rotating the load from a vertically downward position (0 degrees) to a horizontally straight position (270 degrees). i. Derive the equation of motion for the mechanism. Based on this equation, justify why adaptive control is preferable for controlling the position of the load. Utilizing both a flowchart and pseudocode, explain the process of implementing gain scheduling for the purpose of controlling the load's position. iii. Draw the block diagram of the control system. iv. Discuss methods to evaluate the performance of the control system. V. Briefly describe two real practical applications of the statically unbalanced load mechanism. T 1 Mgl Figure 1: Statically Unbalanced Load