Problem $1$: Calibration $(25\text{'})$

Calibration is often required for an instrument before you use it to perform measurements of

interest $-$ this is to ensure the accuracy of the measurements. Dynamic Mechanical Analyzer

$($DMA$)$ is one of the most commonly used instruments to analyze a material's mechanical

properties. But before you perform any testing on a material, you need to do a calibration first.

The calibration kit provides a series of standard weights. Each standard weight represents a

standard force for calibration $(10,20,30,40,50,60,70,80,90N).$ During the calibration, you put

in a standard and record the output force $($ N $).$ Below is the input vs$.$ output table you obtained

from the calibration $($before the equipment is completely calibrated$).$

Please: $(1)$ define the calibration equation so that the output can be the true value of the input;

$(2)$ use Excel to plot the Before$-$Calibration curve and the After$-$Calibration curve in the same

graph, using different line styles to distinguish the before vs$.$ after. When you plot, make sure

to include the labels of $x$ and $y-$axis, units, graph title, legends, and caption of the graph; $(3)$ check

for linearity of the sensor and make comments on if the sensor shows a good linearity.

You must show all of the steps to reflect your working

progress. Only the correct final answer without steps of

calculation will receive a ZERO. You can either write on paper

and submit the scan of your work, or upload the typed file.

Writing must be clear and legible. Please also submit the raw

excel file for maximum credits.