ScholarLens Back to search
2012•Unpublished venueRequires access

ON PERIODIC MOTION OF SIMPLE PENDULUM: "AND YET, IT MOVES."

S. Chatterjee, Smita Pal, S Guha Mallick, West Bengal

Open publisher page 1 citations

Abstract

For solving the nonlinear differential equation of the pendulum, here we adopt a method that transforms the nonlinear differential equation into an equivalent linear one and then evaluate the period oscillation. We also apply the energy conservation principle to find the dependence of the time period on the amplitude of oscillation. Also harmonic balance method is applied to find an expression for the period of oscillation. Theoretical curves, simulation results and experimental results are given in support of the findings. Nonlinear method 1 proves that the pendulum oscillation is periodic but it has also very small amount of third harmonic. FFT analysis has been carried out of the data as obtained from the simulation results and it is found that system is almost free from harmonic distortion. 1. Historical Note:

About this research paper

What this paper is about

For solving the nonlinear differential equation of the pendulum, here we adopt a method that transforms the nonlinear differential equation into an equivalent linear one and then evaluate the period oscillation. We also apply the energy conservation principle to find the dependence of the time period on the amplitude of oscillation. Also harmonic balance method is applied to find an expression for the period of oscillation. Theoretical curves, simulation results and experimental results are given in support of the findings. Nonlinear method 1 proves that the pendulum oscillation is periodic but it has also very small amount of third harmonic. FFT analysis has been carried out of the data as obtained from the simulation results and it is found that system is almost free from harmonic distortion. 1. Historical Note:

Why it matters

OpenAlex reports 1 citations for this work. Citation counts describe recorded attention and do not establish research quality.

Key contribution

A contribution statement is not available in the OpenAlex record.

Method / approach

Method details are not available in the OpenAlex metadata.

Main findings

Findings are not separately available in the OpenAlex metadata.

Limitations

Limitations are not available in the OpenAlex metadata.

Applications

Application details are not available in the OpenAlex metadata.

Available abstract

For solving the nonlinear differential equation of the pendulum, here we adopt a method that transforms the nonlinear differential equation into an equivalent linear one and then evaluate the period oscillation. We also apply the energy conservation principle to find the dependence of the time period on the amplitude of oscillation. Also harmonic balance method is applied to find an expression for the period of oscillation. Theoretical curves, simulation results and experimental results are given in support of the findings. Nonlinear method 1 proves that the pendulum oscillation is periodic but it has also very small amount of third harmonic. FFT analysis has been carried out of the data as obtained from the simulation results and it is found that system is almost free from harmonic distortion. 1. Historical Note:

Key concepts: Pendulum, Simple harmonic motion, Oscillation (cell signaling), Nonlinear system, Mathematics, Harmonic balance, Double pendulum, Kapitza's pendulum

Related papers

Related paper 1Related paper 2Related paper 3
Back to paper searchBrowse research topicsOriginal source
ON PERIODIC MOTION OF SIMPLE PENDULUM: "AND YET, IT MOVES." — Research Paper | ScholarLens