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Simple pendulum

Simple Pendulum Experiment

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Introduction to the Simple Pendulum Experiment

Acceleration due to the gravity of the Earth is denoted by the symbol g which is the acceleration of a body caused by the gravitational field acting on the body towards the center of the Earth, neglecting air resistance and mass. Gravitational acceleration (g) was first determined by Galileo Galilei in 1604. The law of gravitational attraction was formulated by Sir Isaac Newton (1642- 1727) and published in 1687. The magnitude of g varies over the surface of the Earth in which many measurements were undertaken at different locations on the earth.

Aim of The Simple Pendulum Experiment

Calculate the acceleration of free fall by means of simple pendulum.

Tools Of The Simple Pendulum Experiment

·Pendulum bob (metal sphere with hook or hole through it).

·Cotton.

·Stand and clamp.

·Meter scale.

·Stop watch.

·Improvised vice.

Steps And Method of The Experiment

1-Tie a two-metre length of the cotton to the pendulum bob and suspend the cotton from the jaws of an improvised vice, such as two small metal plates held in a clamp.

2-Alternatively two coins, two halves of a cork split lengthwise, or the jaws of a pair of pliers serve equally well for the point of suspension when gripped in a clamp.

3-Place a piece of paper with a vertical mark on it behind the pendulum so that when the latter is at rest it hides the vertical mark from an observer standing in front of the pendulum.

4-Set the pendulum bob swinging through a small arc of about 10°. With a stop-watch measure the time for 20 complete oscillations.

5-setting the watch going when the pendulum passes the vertical mark and stopping it 20 complete oscillations later when it passes the mark in the same direction. Repeat the timing and record both times.

6-Measure the length L of the cotton from the point of suspension to the point of attachment to the bob.

7-Shorten the length of the pendulum by successive amounts of about 10 cm by pulling the cotton through the vice and for each new length take two observations of the time for 20 oscillations.

Parameters, Theory And Final Law of The experiment

The following theory explains how the simple pendulum experiment is used to calculate the acceleration of free fall.

Parameters, Graph & Final Law

T
Periodic time
s
L
Length of pendulum
m
g
Acceleration of free fall
m/s²
PN
Difference between 2 periodic times on graph
s²
QN
Difference between two lengths on graph
m
T²/s² L/m Q N P
Final Law
g = 4π² QNPN m s⁻²

Table of The Readings Of The Simple Pendulum Experiment

Table of the Readings

Length of pendulum
L/m		 Time for 20 oscillations Time for 1 oscillation (periodic time)
T/s		 T²/s²
t1/s t2/s Mean
t/s

Medical Application Of The Simple Pendulum

Understanding the simple pendulum experiment connects directly to how gravity affects human physiology in extreme environments:

Gravity plays a crucial role in physiology. The lack of gravity, like in long duration spaceflight missions, cause pathologies in e.g., the musculoskeletal system, cardiovascular deconditioning, immune system deprivation or brain abnormalities, to just mention a few. The application of artificial gravity through short-arm human centrifugation (SAHC) has been studied as a possible countermeasure to treat spaceflight deconditioning.

Frequently Asked Questions About the Simple Pendulum Experiment

Why must the swing angle be kept small (around 10°)?

The simple pendulum formula assumes small-angle motion, where sin θ ≈ θ. At larger angles, this approximation breaks down and the period calculation becomes less accurate.

Why time 20 oscillations instead of just 1?

Timing a single swing amplifies the effect of human reaction-time error relative to the total time measured. Averaging over 20 oscillations spreads that error out, giving a much more precise value for the period.

Why does shortening the pendulum change the acceleration of free fall calculation?

It doesn't change g itself — g is a property of Earth's gravity, not the pendulum. Taking multiple length-period pairs and plotting T² against L lets you extract g from the slope of the graph, which is more accurate than relying on a single measurement.