a) Model the dynamics of the system completely , i.e., derive the mathematical equations of motion for the system . Hint: Draw the free body diagrams and write the equations for balance of forces for both the trolley and the load. For the load , write the equation for balance of torques (since the load represents a rotational system). b] Based on the derived differential equations J draw a Simulink model of the crane when a pulse input force F of 5 N with duration of 5 seconds is applied to the trolley .Plot the time output of the angular displacement of the load go. Include your Simulink model in the report: with clearly annotated blocks and signal lines . Based on your lab section , you should use the following values for the parameters Secon 3 Section 4 Section 5 0.3 0.25 0.4 Section 2 0.15 Section 1 parameter ml (kg) 1.2 Assume that the friction between the trolley and the rail is negligible , i.e., hr: 0. Hint: Note that you might need to rearrange the differential equations in a form suitable for representation with Simulink blocks . One way to reformulate the model is to express the equations in terms of the highest order derivative of the variables , and use several Simulink integrators blocks to represent the partial derivatives of the variables