Introduction
In this experiment, you can determine the effective length of pendulum with the help of graphs. You should plot two types of graphs, such as L-T and L-T2 graphs.
All you need is a simple pendulum graph. Calculation of effective length is a very significant and sensitive experiment. Students should go for the error-free values to determine the right parameter at the end.
This article is completely based on simple pendulum experiment readings and graph. Students can gain a brief idea about this experiment after reading the article.
Materials or Apparatus Required
Some of the materials that are listed below for the second’s pendulum experiment:
Split Cork
Clamp stand
Long and strong cotton thread
Heavy metallic spherical bob with a hook
Meter scale
Graph Paper
Stopwatch
Pencil Eraser
Principle of Simple Pendulum Experiment
This experiment has the objective to find the time of a simple pendulum. Also, the length of the second’ pendulum can be calculated within the same operation. Simple harmonic motion on a simple pendulum exhibits an acceleration.
As you know, the acceleration of the pendulum’s bob is directly proportional to the displacement from the mean position. The time is the value that we need to determine for the simple pendulum.
The relation of time is given below:
T = 2π √(L/G)
Procedure
Keep the clamp stand over the table. Attach the pendulum bob with a hook. The length of the string is about 150 cm. another string is two half-pieces of a split cork.
Attach the cork tightly with the clamp. This allows a better line of separation between the two pieces of the split cork at right angles to the line OA. When the pendulum oscillates, you can notice the change.
Identify the edge of the table that the pendulum is reaching. Mark the lines that lie beyond the edge of the table (about 2 cm above the floor). Mark the line that comes just behind the vertical thread OA.
After the setup, you can measure the length of the simple pendulum.
Students must consider some of the effective length L along the x-axis. Also, consider the y-axis of value T2 (or T) for plotting the graph. Some of the experiential values from the table are taken into consideration.
Choose convenient scales on these axes to present L and T2 (or T). A graph that is plotted between L and T2 and also between L and has the impact.
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Observation
From the above setup, students should verify the details and answer the following parameters to get appropriate outputs. The following points are given for considering them:
Length of the hook = __ cm
The pendulum's radius of the bob = __ cm
The least count of the stopwatch = __ s
The least count of the meter scale = __ mm
How to Plot the Graphs?
The simple pendulum graph is here as shown:
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i) L Vs T Graph
You can plot the graph between L~T to observe different outputs. A table can be helpful to note down all outputs. You can take L along the x-axis and T along the Y-axis. From the figure, you can notice that the graph will give you a curve line.
ii) L Vs T2 Graph
You can plot the graph between L and T3. All of the results can help you further if you keep them in a tabular form. The output of the relation will give you a straight line, as shown in the figure.
iii) We can find out the effective length of the second’s pendulum for T2 = 4s2 obtained from the second graph.
The Output of the Experiment
From the above experiment, you can obtain three output which is given below:
A curve that comes out of the L-T graph gives rise to convex upwards.
A straight line is obtained from the L – T2 graph.
Viva Questions
1. How Do You Define the Connection Between Frequency and Time?
Answer: The connection between frequency and time period is given by the following expression,
f = 1/T
2. How Do You Define the Restoring Force?
Answer: Restoring force is a force that helps to bring back the vibrating body towards the mean position. This force acts as the resistance force for the body that vibrates.
3. Is it Useful to Use a Cricket Ball Instead of the Bob in a Pendulum?
Answer: No, this is not that good. The bob must be lighter and smaller. A cricket ball can’t be the possible reason for the replacement period.
4. Why Don’t We Use a Rubber Band by Replacing the Thread?
Answer: No, this is not the way we should experiment. The rubber band is not inextensible like a thread. So, we keep the thread on a priority basis.
FAQs on To Find Effective Length of Seconds Pendulum Using Graph
1. What is a seconds pendulum?
A seconds pendulum is a pendulum whose time period (T) is exactly two seconds. This means it takes precisely one second to swing from one extreme position to the other and another second to complete the return swing.
2. What is the primary objective of using a graph to find the effective length of a seconds pendulum?
The main objective is to experimentally verify the relationship between the square of the time period and the length (T² ∝ L). By plotting a graph of L vs T², one can accurately determine the effective length (L) corresponding to a time period of 2 seconds and also calculate the value of acceleration due to gravity (g).
3. What is the formula that connects the time period (T) and effective length (L) of a simple pendulum?
The relationship is defined by the formula T = 2π√(L/g), where T represents the time period, L is the effective length, and g is the acceleration due to gravity. For graphical analysis, this is often expressed as T² = (4π²/g)L, which shows a direct linear relationship between T² and L.
4. How do you determine the effective length of a seconds pendulum from an L vs T² graph?
After plotting the L vs T² graph with effective length (L) on the x-axis and the square of the time period (T²) on the y-axis, you follow these steps:
- Since a seconds pendulum has a time period T = 2s, the corresponding T² value is 4 s².
- Locate T² = 4 on the y-axis of your graph.
- From this point, draw a horizontal line to intersect your plotted straight line.
- From the point of intersection, draw a vertical line down to the x-axis.
- The value where this vertical line meets the x-axis is the effective length of the seconds pendulum.
5. Why is the L vs T² graph preferred over the L vs T graph in this experiment?
The L vs T² graph is preferred because it produces a straight line that passes through the origin, which is much easier to analyse. In contrast, the L vs T graph results in a parabolic curve. A straight-line graph allows for a more reliable and accurate calculation of the slope, which is essential for determining related physical quantities like 'g' and makes it simpler to read values from the graph.
6. What is the physical significance of the slope of the L vs T² graph?
The slope of the L vs T² graph holds direct physical significance as it is related to the acceleration due to gravity (g). Based on the equation T² = (4π²/g)L, the slope of the graph (which is ΔT²/ΔL) is equal to 4π²/g. Therefore, by calculating the slope from the experimental graph, you can determine the value of 'g' using the formula g = 4π² / slope.
7. Why is it important for the string of a simple pendulum to be inextensible and the bob to be small and heavy?
These properties are crucial for the experiment to match the ideal simple pendulum model for which the formula is derived:
- Inextensible String: The length (L) of the pendulum must be constant during oscillations. An elastic string would stretch, causing L to change and making the time period inconsistent.
- Small and Heavy Bob: A small, spherical bob helps to minimise air resistance. A heavy, dense bob ensures that its centre of mass is well-defined and its mass is significantly greater than the string's mass, allowing the string's mass to be ignored in calculations.
8. What are some common sources of error in the simple pendulum experiment and how can they be minimised?
Some common sources of error include:
- Reaction Time Error: Inaccuracy in starting and stopping the stopwatch. This is minimised by timing a large number of oscillations (e.g., 20 or 30) and then calculating the average time for one oscillation.
- Non-planar Oscillation: The bob may swing in an ellipse instead of a single plane. This is minimised by releasing the bob gently without any sideways push.
- Large Amplitude: The formula T = 2π√(L/g) is only accurate for small angles. The amplitude of the swing should be kept small (less than 10 degrees) to ensure the motion is approximately simple harmonic.
