Exercise 1

# Exercise 1 - Exercise 1 Warmup on using MATLAB The table...

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Exercise 1: Warmup on using MATLAB The table below displays voltage measurements V i (T i ) performed for one period of a periodic waveform (i=1:21): T i (sec) V i (volts) ______ _______ 0 0.041 0.05 0.128 0.1 0.449 0.15 0.748 0.2 0.785 0.25 0.831 0.3 0.774 0.35 0.643 0.4 0.606 0.45 0.187 0.5 0.067 0.55 -0.332 0.6 -0.604 0.65 -0.688 0.7 -0.840 0.75 -0.818 0.8 -0.834 0.85 -0.640 0.9 -0.567 0.95 -0.179 1 -0.080 Prepare a MATLAB m-file to load the above data file and perform the following operations : (1): Using the MATLAB functions polyfit and polyval, determine the coefficients of polynomials of orders 2, 3, 4, and 5 V F (T) = A 0 + A 1 *T + A 2 *T 2 + • fit to these data. (2) The residuals δ i are the differences V(T i ) - V F (T i ) between the voltage measurements V(T i ) and the values V F (T i ) given by the fitting. The RMS deviation ΔV between the measurements and the values predicted by the fitting is given by the expression:

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(ΔV) 2 = ∑ (δ i ) 2 /N where i=1:N and N is the total number of measurements. (2a) Calculate the RMS deviations ΔV for each of the 4 polynomial fittings and write these values in your lab notebook. The “best fit polynomial” is the fitting that gives the smallest RMS deviation.
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