Vibrating Cantilever

VIBRATING CANTILEVER AIM: The aim of this experiment is to investigate the factors that affect the period of oscillation

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VIBRATING CANTILEVER AIM: The aim of this experiment is to investigate the factors that affect the period of oscillation of a cantilever and also to suggest equations by which they might be related. There are TWO parts: (i) variation of length with a fixed mass on the end of the cantilever (ii) variation of mass while keeping the length of the cantilever fixed.

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YOU WILL NEED: A G clamp, a metre ruler, a set of slotted masses (0 – 1 kg), a stopwatch, a pencil or biro, a rubber band WHAT TO DO: For both experiments the apparatus is set up as shown with one end securely clamped to the bench. Do not the load beam too greatly. Make measurements of the period of oscillation (T) for both experiments over a range of either length (L) or mass (M). ANALYSIS AND CONCLUSIONS: Using your results plot two graphs, one of lgT against lgM and the other of lgT against lg L. From your results suggest a possible equation for the motion. As an extension to the experiment you can use your results to calculate the Young modulus for the material of the vibrating beam. If a metre rule is used with a thickness d and width b: Young modulus (E) = [162ML3]/[bd3T2]