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Mechanical Spring Deflection

Some tests are run where a ball of a fixed mass dropped from a known height to land inelastically onto a spring whose maximum compression is recorded. The data collected from tests runs at several heights will be contained in a text file $($in the same folder as your Matlab code$)$ called CompressionVersusHeight.txt$,$ an example of which is available on CatCourses. Note that the data file can have any number of data points after the three header lines and any script that reads it must be able to read different versions without change to the script. A plot of the example data is shown.

Write a single$-$file Matlab script that reads the data from CompressionVersusHeight. txt$.$ Then, use Matlab's curve$-$fitting function to find a curve of the form $\backslash ($ y$=$A $\backslash$sqrt$\{$x$\}\backslash )$ that best fits the data. Make sure that your code assigns the value of the value of Ato a variable called A$.$ On a single figure, plot the original data with markers and the fitted curve on the same plot, with a legend, appropriate axis labels and indicate clearly in the plot title the value obtained for $\backslash ($ A $\backslash ),$ with four digits after the decimal place.

Hint: This is most easily done using the custom curve fit technique discussed in the lecture notes.

A sample of the resulting plot for a slightly different data set is shown below.

Write a single$-$file Matlab script that reads the data from CompressionVersusHeight. txt$.$ Then, use Matlab's curve$-$fitting function to

find a curve of the form y$=$Asqrtx that best fits the data. Make sure that your code assigns the value of the value of Ato a variable called

A$.$ On a single figure, plot the original data with markers and the fitted curve on the same plot, with a legend, appropriate axis labels and

indicate clearly in the plot title the value obtained for A$,$ with four digits after the decimal place.

Hint: This is most easily done using the custom curve fit technique discussed in the lecture notes.

A sample of the resulting plot for a slightly different data set is shown below.

Data with x$=$A$**$ sqrt$($h$)$ curve fit

A$=0\mathrm{.}9836$

reads data

Error using fit$>$iFit $($line $233)$ X$,$ Y and WEIGHTS cannot have NaN values. Error in fit $($line $117)[$fitobj$,$ goodness, output,

convmsg$]=$ iFit$($ xdatain, ydatain, fittypeobj, $...$ Error in solution $($line $9)$ fitResult $=$ fit$($h$,$ x$,$ model, 'StartPoint', startPoint$)$; $\%$

Fit the data using the model

Data must be read from 'CompressionVersusHeight.txt$\text{'}$

Feedback is shown for the initial error only, as subsequent failures may be due to the first error Show Feedback

check coefficient

check plot title

check plot legend