Take the bob of the pendulum to one side so that the pendulum makes \(5^{\circ}\) with the vertical and release the bob. Start the stop watch when the bob is at the mean or extreme position and find the time taken by the pendulum to complete 20 oscillations. Dividing the time for 20 oscillations by 20 gives the time period (T) of the pendulum. The above experiment can be repeated for different lengths \((80 \mathrm{~cm}\),

The time period (T) of a pendulum is a fundamental aspect of its motion, referring to the time it takes for the pendulum to complete one full swing back and forth. Calculating the time period accurately is crucial because it allows us to understand the pendulum's oscillation in relation to time.

To calculate the time period, as outlined in the experiment, one must record the time for a number of oscillations. In this case, we measure the time for 20 complete back and forth swings using a stopwatch starting from when the pendulum bob is at its mean position (the lowest point) or extreme position (the highest point in the swing on either side). As given in the solution, the time period is obtained by using the formula:
\[ T = \frac{t}{n} \]
where \( t \) is the total time recorded for \( n \) oscillations. It is important to ensure that the start and end points for timing are consistent. For precision, multiple trials are recommended to minimize errors. Regular practice with these calculations helps develop proficiency in dealing with oscillatory motion systems.

Effective physics laboratory techniques are pivotal for obtaining reliable results in experiments like the pendulum oscillation. You must begin with a proper setup, ensuring that the pendulum is securely fixed at a point and that the string or rod has negligible mass compared to the bob.

When performing the experiment you should:

• Use a protractor to set the initial displacement angle to precisely \(5^{\text{o}}\).
• Start and stop the stopwatch with precision when the pendulum passes the mean or extreme position.
• Record the data meticulously after each set of oscillations for different lengths of the pendulum.
• Take multiple measurements to average out human error in timing.

The best practices in the laboratory also involve careful observation, avoiding parallax errors while reading measurements, and ensuring that external factors like air resistance and friction at the pivot are minimized.

Simple harmonic motion (SHM) is characterized by an object's oscillation about an equilibrium position, where the restoring force is directly proportional to the displacement from this position. A classic example of SHM is the motion of a simple pendulum provided that the angular displacement is small.

In SHM, the time period is dependent on the properties of the system, such as the length of a pendulum and the acceleration due to gravity, but is independent of the amplitude of the oscillations, provided this amplitude is small. The time period of a simple pendulum is given by the equation:
\[ T = 2 \pi \sqrt{\frac{L}{g}} \]
where \( T \) is the time period, \( L \) is the length of the pendulum, and \( g \) is the acceleration due to gravity. SHM is an important concept in physics as it can describe a variety of phenomena, from the oscillations of atoms in a crystal lattice to the movement of celestial bodies.

Graph plotting is a crucial skill in physics that helps visualize the relationship between different physical quantities. A well-plotted graph can reveal patterns or underlying principles governing the behavior of the system being studied.

In the pendulum experiment, plotting the graph of the time period (T) against the length (L) allows us to visually analyze the dependency between these two quantities. On a graph, we typically place the independent variable (length, L) on the x-axis and the dependent variable (time period, T) on the y-axis.

By plotting the data points for each length and connecting them, we can see if the relationship is linear or nonlinear. A curve represents a nonlinear relationship, suggesting that T varies with some function of L. From our understanding of a simple pendulum, we anticipate a square root relationship, which would produce a parabolic curve on a graph. Through graph plotting, complex relationships become more understandable, enabling us to extrapolate or interpolate data, which is a significant technique for physicists.