Write a Note on Simple Pendulum Experiment

The pendulum is a mass that is hung from a hinge and swings freely. Whenever a pendulum is moved laterally from its sitting position or mean position, gravity acts as a restorative force, accelerating it back to the equilibrium location. The restoration reaction force here on the pendulum’s weight leads it to cycle out about equilibrium position, swaying back and forth when the pendulum makes it oscillate about the neutral position, swinging front and back when it is unleashed. The interval is the amount of time it takes to complete a full cycle, which includes both left and right swinging. The time is based on the pendulum‘s length and, to a lesser extent, by the amplitude, or the breadth of the swing.

Coming to a simple pendulum it is a single point mass hung by a massless thread from a location around which it is permitted to shift front and back in space. When contrasted to the mass and length of the thread in which it is hung, a basic pendulum could be represented by a tiny ball with a specific diameter and a big mass.

Simple Pendulum Experiment

A simple pendulum experiment is a set of apparatus taught in class 11th in almost every education board. Where the students get to learn about the pendulum and its associated topics such as finding the timing of the pendulum, how the motion of the pendulum takes place, and many others.

The apparatus consists of a tiny metal sphere along with a thread with known length, a stand on which the thread can be hung (a clamp with a stand), a split cork, vernier callipers for measurement, a stopwatch to measure time and a half meter scale.

Theory

As we’ve understood about the simple pendulum, what it is and how it works, we’ll directly move into the theory that needs to be understood by the student during the practical experiment of a simple pendulum.

In the experiment the spherical bob can be called as point mass denoted by G and the distance between the bob and the suspension can be called the pendulum’s effective length which includes the radius of the bob, the length of the hook along with the length of the thread used.

The formula of effective length will be,

L=l+h+r

Where,

L = string length

h = hook’s length

r = bob’s radius

The formula of the time period

The finding of the period plays an important determination in the experiment of a simple pendulum and is also said as the time period formula. It produces an SHM, which stands for Simple Harmonic Motion. An SHM is produced by the relation between the acceleration and the position of the bob, which is as the acceleration is directly related or proportional to the mean position of the bob and which is directed towards it only. So, the time period formula for cycles having small amplitudes is,

T=2Lg

Where,

T = Time 

L = Length of the string

g = acceleration due to gravity

Procedure for Simple pendulum Experiment

         The procedure for the experiment goes on as initially all the callipers and measurement instruments should be brought to their zero value or their zero error should be corrected. And then the measurement of the apparatus such as the body diameter, length of the string, etc. is calculated and noted.

         When the measurements are known, adjust the length of the string to make the mean effective length an integer value, which will ease the calculations using its formula. Later change the length of the thread and note a few readings of it to plot a graph at the end. Such as the initial reading be L1, measure L2, L3, L4, etc. also along with it as per the need and the experiment. As given in the below figure.

         Now, hung the bob tied with threads in the stand with the help of split cork at mark L1, to allow the bob to swing back and forth. There should be always a gap between the base and the bob.

         Considering the figure below, After the setup, marking of a line AC should be done on the table to understand the length of oscillation having its centre as B which is the mean position of the bob.

         During this time get ready to take the measurements as all the setup is done. So, to take the measurement, hold the bob and move to position C and release it. When the bob crosses its mean position and goes to point A, and back to C and then to Bone cycle completes (from B to A to B to C and back to B). Count 20 such oscillations or cycles. And during the start of bob passing its mean position start the stopwatch till its 20th oscillation and note down the reading.

         Now, do the same procedure with length L2, L3, and others of the string and measure the timing for 20 oscillations with their respective timings.

         In the end, plot the L-T (Length or thread and their time) graph and similarly L-T^2 graph. which is said the be the outcome of a simple pendulum experiment pendulum

The conclusion/outcome would be that the pendulum travels a larger range in less time and has a relatively short time frame than a shorter range. Galileo believed the period remained constant for a variety of reasons. Friction was one aspect that Galileo overlooked.

Conclusion

         A pendulum is a mass hung with a string on a stand and a simple pendulum experiment is a simple experiment to relate the change in length of the time and its square against the various lengths of the string practically.  The time and the length should be noted during the experiment to make the graph. The graph should have a curve line in the L-T graph and a straight line in the L-T^2 graph. Which will result in the successful completion of the experiment.

         Some precautionary measures to take care of would be to have a tight and strong string, there should not be any vibration in the stand, etc. to properly get the values and prepare the graph correctly.