Estimation of the error matrix in a linear least square fit to the data from an experiment performed by smartphone photography

• DOI: 10.48550/arxiv.2307.12312
• Publication Date: 2023-01-01
• Authors: Sanjoy Kumar Pal; Soumen Sarkar; Surajit Chakrabarti
• Keywords: Bar (unit)

Determination of the Young modulus a metal bar in form cantilever is an old experimental concept. However, we have taken advantage modern advanced technology smartphone camera to find load depression graph by taking photographs with camera. Smartphone photography allows us precise transverse magnification object from size real image formed on sensor Image can be obtained micron level accuracy. From graph, determined bar. The sensitive measurements at its free end own weight, allowed determine density aluminium. We added analysis chi squred minimisation technique for determining parameters and their uncertainities linear fit. Starting curvature matrix made comprehensive error relevant two parameter Then shown how fitted which includes covariance term between correlated parameters, context our specific experiment. propagated errors uncertainties that measurement possible photography.