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Internal Code: MAS1908
MATLAB Codes Assignment:
Task:
Introduction
A type of electrical switch can be modelled as a simply-supported beam (Fig. 1), where the middle of the switch is pushed down until it makes contact and completes the circuit. Measurements have been made of the deflection of the switch; these measurements have been averaged at each location, with the averages stored in the file ass3q1in.csv.
Requirements
For this assessment item, you must perform hand calculations:
1. Derive the formulae for the slope (v’), curvature (v ”) and v”’ of the beam from Eq. (1).
2. Estimate the value of the slope at the second measurement point using backward, forward and central differences.
3. Validate your answers from Requirement 2 using the appropriate formula from Requirement 1.
4. Estimate the numerical errors in the calculations of Requirement 2 using the appropriate formulae from Requirement 1. What is the ratio of (the numerical error) to (the deviations from the theoretical values calculated in Requirement 3)? Be careful to get the sign consistent between the errors (i.e. that you compare the same thing)!
5. Discuss which is the best result out of the backward, forward and central differences and why.
You must also produce MATLAB code which:
6. Calculates backward, forward and central differences for the length of the beam.
7. Verifies the results from Requirement 6 using the results of Requirement 2.
8. Calculates the theoretical values at the measurement locations using the appropriate for- mula from Requirement 1. Calculates the error between the numerical and theoretical values.
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