Aim	The aim of this experiment is to find the effective length of a second’s pendulum using the L-T and L-T^2 graphs.
Apparatus Required	A simple pendulum consisting of a small weight and a thread or string A stopwatch or timer A ruler or measuring tape A stand or clamp to hold the pendulum A piece of graph paper A pen or pencil
Theory	A simple pendulum consists of a small weight suspended from a string or thread, which is free to swing back and forth under the influence of gravity. The motion of a simple pendulum is periodic, meaning that it repeats itself after a fixed time interval known as the period (T). The period of a pendulum depends on the length of the pendulum (L) and the acceleration due to gravity (g), and is given by the equation: T = 2π √(L/g) In this experiment, we use a stopwatch or timer to measure the time taken for the pendulum to complete one full swing (i.e. to return to its starting point). By varying the length of the pendulum and measuring the corresponding values of T, we can plot a graph of L against T and L against T^2. The gradient of the L-T^2 graph is equal to 4π^2, and the effective length of a second’s pendulum is given by the length at which this gradient is equal to 4π^2.
Procedure	Set up the pendulum by attaching the weight to the thread or string and hanging it from a stand or clamp. Measure the length of the pendulum from the point of suspension to the center of mass of the weight using a ruler or measuring tape. Record this value as L. Set the pendulum in motion by pulling the weight to one side and releasing it. Use a stopwatch or timer to measure the time taken for the pendulum to complete one full swing (i.e. to return to its starting point). Repeat step 3 several times and calculate the average time taken for one swing. Record this value as T. Repeat steps 3 and 4 for different lengths of the pendulum by adjusting the length L and measuring the corresponding values of T. Record these values in a table. Using the values of L and T, plot a graph of L against T. Using the values of L and T, plot a graph of L against T^2. Draw the best-fit straight line through each graph. Measure the gradient of each graph. The effective length of a second’s pendulum is given by the length at which the gradient of the L-T^2 graph is equal to 4π^2. Record the effective length of the second’s pendulum and compare it with the actual length of the pendulum.
Observation and Result	During the experiment, we observe that the time period of the pendulum is dependent on the length of the pendulum, and is given by the equation T = 2π √(L/g). As we increase the length of the pendulum, the period of oscillation also increases, which means that the pendulum takes longer to complete one full swing. By plotting the values of L and T on a graph, we can observe a linear relationship between L and T. The slope of this line can be used to determine the value of g. When we plot L against T^2, we observe a linear relationship between these variables as well. The slope of this line is equal to 4π^2, which allows us to calculate the effective length of a second’s pendulum using the equation L = (T^2 g) / (4π^2). We can compare the effective length of the pendulum with its actual length to determine the accuracy of our measurements. Overall, this experiment demonstrates the relationship between the length and period of a simple pendulum, and allows us to calculate the effective length of a second’s pendulum using simple graphical techniques.