The Simple Pendulum

European Journal of Physics, 2005

We describe a 8085 microprocessor interface developed to make reliable time period measurements. The time period of each oscillation of a simple pendulum was measured using this interface. The variation of the time period with increasing oscillation was studied for the simple harmonic motion (SHM) and for large angle initial displacements (non-SHM). The results underlines the importance of the precautions which the students are asked to take while performing the pendulum experiment.

Physics Education, 2013

Geometric demonstration located in v, t diagram explains the nature of the period of a pendulum, i.e. the universal connection of time with velocity (radius) and acceleration. Conceptual nature of the principles proof points to its universal validity. In other words, if it is valid for a circle, it is valid. Through the geometry of free fall we describe physical

Introduction The time period of a pendulum is related to its length, the longer the pendulum the longer is the time period, however you might not know that the period is also related to the gravity. If you took a pendulum to the moon, it would swing more slowly so have a longer time period. In this experiment I will measure the acceleration due to gravity on earth by measuring the time period of a pendulum

• General Background: A mass m hanging from a string whose length is L and a pivot point on which this mass is fixed are what a simple pendulum (which was discovered during the 10 th century by Ibn Yusuf) consists of. During the 17 th century, it is developed by some physicist, especially by Galileo. When the mass hanging from the string is released with an initial angle, it starts to move with a periodic motion. The motion can be approximated as a simple harmonic motion if the pendulum swings through a small angle (so sin (ө) can be approximated as ө). The frequency and period for the simple pendulum are the independent of the initial angle of the movement (initial position of the mass to the vertical reference line). In addition to the initial angle of the mass, the period doesn't depend on the mass of the object. However, it is affected by the length of the string which the mass is hanged on and the acceleration of gravity. The most widespread applications of the simple pendulum are for timekeeping, gravimetry (the existence of the variable g in the period equation of simple pendulum-• means that the pendulum frequency is different at different places on Earth), seismology, scholar tuning, and coupled pendula. It is also used for entertainment and religious practice. • Aim: To determine the effects or contribution of the length of the string on the period for the simple pendulum and find out a mathematical relationship between the length and the period. • Hypothesis: Since the length of the string which the mass is hanged on is shortened, the magnitude of the period for the simple pendulum gets increased. Different masses of the object hanging from the string have no effect on the period.

CUADERNOS DE EDUCACIÓN Y DESARROLLO, 2023

In this study, with a pedagogical aim suited for the undergraduate, the differential equations of motion that characterize and determine the motion of a simple pendulum were obtained considering small and large amplitudes of oscillation. These differential equations were solved through differential equation solution methods, numerical, expansion of functions and integrations. The solutions obtained using the different methods were compared. It was possible to verify, both experimentally and theoretically, that for the oscillatory movement of the simple pendulum, its oscillation period increases and its angular frequency decreases with the increase of the oscillation amplitude. The validity range of the approximation for small ranges of motion was also determined. It was verified that the theoretical and experimental results present a good agreement for angles smaller than 55°. The experimental measurements were made with "a low-cost home-built" equipment.

2023

A simple pendulum consists of an inextensible wire to which a point mass m is attached. Moved away from its vertical position by an angle θ and abandoned to the gravity action, it begins to oscillate on either side of this position.

Many first year university students in the Science related fields have a problem in identifying and applying the fundamental mathematical concepts that they have learnt from as far back as Grade 10 in solving some of the physics related problems. The majority of students, mostly from public schools, cannot seem to relate the two fields of study. Previous studies have shown that majority of first year students lack the integrated approach to different scientific disciplines in solving some specific problems and in experimental analysis. This paper presents the findings of an investigation on the ability of the first year students to use the mathematical concept of the straight line equation and graph, in analysing physics properties, with particular reference to a Simple Pendulum motion experiment. The method employed was experimental. Students were given a simple pendulum experiment to determine the gravitational acceleration of the pendulum by graphical analysis. Two graphical approaches were employed, with both expected to yield the same results. Participants were required to analyse the motion of the pendulum, specifically the variation of the length of the pendulum with the period of oscillation. The feedback showed a far reaching implications relating to first years’ abilities to mathematically analyse a physics concept. These findings serve as a basis for a need to improve the teaching of science and mathematics in the schools, especially the practical approach to teaching and learning science.

American Journal of Physics, 2006

A simple approximate formula is derived for the dependence of the period of a simple pendulum on the amplitude. The approximate is more accurate than other simple formulas. Good agreement with experimental data is verified.