# Compound Pendulum Essay

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Procedure 3: The Compound Pendulum The aim of this experiment is to determine the value of the acceleration due to gravity by measuring the period of oscillation of the pendulum when suspended from different distances from its centre of mass. A pendulum consisting of any swinging rigid body which is free to rotate about a fixed horizontal axis is called a compound pendulum. This experiment had to be carried out at Glasgow University as the required equipment was not available at school. Procedure 1) The pendulum was balanced on a large brass knife edge to determine the position of the centre of mass of the pendulum. 2) The larger moveable knife edge was then clamped to the pendulum, at a small distance (1cm) above the centre of mass. 3) The distance h was then determined from the centre of mass to the axis of suspension. 4) The mask was then attached to the pendulum. 5) The light gate was then connected to the digit-metre and adjust its height and position relative to the mask to allow the period T, of the pendulum to be measured repeatedly. 6) The procedure was then repeated for larger values of h, until T has passed its minimum value. (A smaller moveable knife edge must be used for values of h, as the axis of suspension lies on the narrow strip region of the pendulum) 7) A graph of T against h was then plotted and the value of h at which the period reaches a minimum should be estimated. 8) A graph of hT2 against h2 was then plotted and analysed to obtain a value for g. As a means of obtaining the value for g, the results were used to produce a straight line graph and the gradient of the graph used to find the value of g. The period of the pendulum is given by; T=2πω=2π(k2+h2)gh Squaring both sides of this equation gives; T2=4π2ghk2+h2 This re-arranges to give; hT2=4π2g×h2+4π2g×k2 Which is the form y=mx with y=hT2,