Question 6 - Basic curve-fitting, symbolic math and plotting. [14 Marks] 6.1 The file torque_speed_curve.txt contains the speed, torque and power data for the DC generator from the question above. It contains 3 columns of data, the first is the generator speed in rad/s, the second is the required torque of the generator at each corresponding speeds in Nm and the third is the power COMPUTERS IN ENGINEERING ANALYSIS Assessment Paper 2024 MECH101001 Page 5 generated in mW. The delimiter for the file is a tab. Read in the data in columns 1, 2 and 3 and set to variables speed, torque and power respectively. Convert speed from rad/s to rpm and convert power generated from mW to W (all should be column vectors). [2 mark] 6.2 The relationship between speed and torque is a second order polynomial. Use the polyfit function to determine the relationship such that torque = a*speed² + b*speed + c. Assign the calculated coefficients to a vector variable coeffs. [2 marks] 6.3 Using the symbolic maths toolkit, create 5 symbolic variables t, v, a, b, c. Then create a symbolic equation, t= a*v² + b*v + c assign to a symbolic variable torque_eqn. [2 marks] 6.4 You are going to solve the equation to find the speed in RPM which corresponds to a torque of 0.7Nm. Substitute 0.7 fort, and the three coefficients derived in 6.2 for the symbolic variables a, b and c respectively into the symbolic equation in torque_egn. Assign the resulting symbolic equation to a variable torque final (do not overwrite torque_eqn). [2 marks] 6.5 Now solve the symbolic equation torque_final for v. As a quadratic there will be two solutions for v. Select the positive solution (the second value) and convert to a double and assign it to the variable operating_speed. [2 marks] 6.6 Now we have the operating speed in RPM we want to use this to determine the power generated. You can use the function interp1 to do this. It is a built in MATLAB function. Type help interp1 to give details of the function. For the operating speed value, determine the power in W that is generated at a torque of 0.7Nm. Assign to a variable operating_power. [1 mark] 6.7 Using the figure below, create a plot of the power generated against speed and mark the operating point determined in 6.6 on the figure with a red circle. Label the plot appropriately including a title. [3 marks]

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Question 6 - Basic curve-fitting, symbolic math and plotting. [14 Marks] 6.1 The file torque_speed_curve.txt contains the speed, torque and power data for the DC generator from the question above. It contains 3 columns of data, the first is the generator speed in rad/s, the second is the required torque of the generato