Measuring Young's Modulus: Clamped vs Freely Supported Ends

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To measure Young's modulus by analyzing beam deflection under a point mass, the placement of the beam's ends is crucial for precision. Using both freely supported ends can lead to displacement of the reference point during deflection, which may affect accuracy. Conversely, clamped ends, or fixed ends, do not allow for bending moments at the supports, theoretically providing different stress and deflection characteristics. The choice of support configuration will influence the results, as each setup presents unique advantages and disadvantages. Ultimately, the beam can be supported in various ways, but the specific arrangement will determine the precision and reliability of the measurements taken.
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I have a project to measure young modulus by measuring the deflection of a beam under point mass. I have derived the equation but i am confused to how the end of beam should be placed to obtained best precision. Should it be both clamped end, freely supported end or a mixture of both?

My idea so far is that for both freely supported ends, its disadvantage is the reference point of x=0 might be displaced during deflecton. However, i can't think of the both clamped scenario disadvantages
 
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By clamped and do mean fixed end? By such test useally the and is free (support doesn't take any banding moments). Teoretecly u can support your beam as you want. You will have differnet stresses and different deflections.
 
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