This example lab report is for an experiment that attempts to determine the acceleration of gravity using a pendulum. Determining the acceleration due to gravity Aim To determine the acceleration due to gravity g using a simple pendulum. My hypothesis is that the acceleration due to gravity is proportional to the square of the period and has a value close to 9.8 ms-2. Theory A simple pendulum consists of a small weight suspended from a thread that is allowed to swing about a suspension point, as shown in Fig 1. The period T is the time for one complete swing, when the weight returns to its original position and velocity. The length of a simple pendulum L is measured from the suspension point to the middle of the weight. Provided the total angle of swing is, <10Ā°, T and L are related by T = 2 x V (L/g) [1] ā¬ 20 T (s) ā¬ L where g is the local acceleration due to gravity. (Wolfson p210) g Taking the square of both sides and rearranging gives Figure 1: a simple pendulum is sketched swinging one complete period T T2 = 4 x2 L/g = (4 x2 / g) L [2] This is of the form of a linear equation y = mx. Values of T are measured for a range of L-values, and a graph of T2 vs L is plotted, yielding a straight line of best fit. As the gradient of this straight line is given by m = 412 / g, the value for g can be determined from the measured gradient m. The uncertainty in m, Am is also determined from the graph using | N|XN-X_1| [3] Am = where x and y are the coordinates of each measurement and y' is the y coordinate of the line of best fit. From an analysis of the uncertainties in the equation m = 4 12 / g we obtain 4g / g = Am/ m, from which Ag is then determined. Method A small brass cylinder with a hole through it was slid onto a length of cotton with a knot at one end. The other end was gripped by a clamp on the retort stand. The lab supervisor gave each group a value for L which was used to the length of the string (0.7 m). Each group then measured the time for 5 swings being careful to keep the angle low (< 10Ā°). We repeated the measurement a few times to ensure there was experimental consistency and we averaged these measurements once confident in our procedure. Diving this time by 5 yielded our period and this was shared with the class, with the class results used in the Table 1. Results F us For five different lengths the period T were experimentally determined. Squaring these values Table 1: row 5 allows a graph of T2 vs L to be made Graph 1 (below). The line of best fit y values from the graph were written