相关论文: Simple Pendulums in Simple Harmonic motion
The motion of a pendulum is described as Simple Harmonic Motion (SHM) in case the initial displacement given is small. If we relax this condition then we observe the deviation from the SHM. The equation of motion is non-linear and thus…
Pendulums have long fascinated humans ever since Galileo theorized that they are isochronic with regards to their swing. While this simplification is useful in the case of small-angle pendulums due to the accuracy of the small-angle…
In this work we solve the nonlinear second order differential equation of the simple pendulum with a general initial angular displacement ($\theta(0)=\theta_0$) and velocity ($\dot{\theta}(0)=\phi_0$), obtaining a closed-form solution in…
The classic simple pendulum is a device which works as a simple harmonic oscillator (S.H.M.) only approximately. The time period remains fixed as long as the amplitude is kept sufficiently small. This limitation makes it unsatisfactory…
In this paper, we handle the problem of the motion of the Foucault pendulum. We explore a new method induced from the De Alembert Principle giving the motional equations without small-amplitude oscillation approximation. The result of the…
We discuss the equation of motion of the driven pendulum and generalize it to arbitrary driving angle. The pendulum will oscillate about a stable angle other than straight down if the drive amplitude and frequency are large enough for a…
The Fourier-based analysis customarily employed to analyze the dynamics of a simple pendulum is here revisited to propose an elementary iterative scheme aimed at generating a sequence of analytical approximants of the exact law of motion.…
The period of oscillation of a simple pendulum ($T = 2\pi\sqrt{l/g}$) is a familiar formula to the average first-year physics student. However, deriving this expression from first principles involves solving a non-linear differential…
The change of the plane of oscillation of a Foucault pendulum is calculated without using equations of motion, the Gauss-Bonnet theorem, parallel transport, or assumptions that are difficult to explain.
A simple approximation formula is derived here for the dependence of the period of a simple pendulum on amplitude that only requires a pocket calculator and furnishes an error of less than 0.25% with respect to the exact period. It is shown…
Small oscillations evolved a great deal from Klein to Robinson. We propose a concept of solution of differential equation based on Euler's method with infinitesimal mesh, with well-posedness based on a relation of adequality following…
This paper presents a general formulation of equations of motion of a pendulum with n point mass by use of two different methods. The first one is obtained by using Lagrange Mechanics and mathematical induction(inspection), and the second…
The looping pendulum is a simple physical system consisting of two masses connected by a string that passes over a rod. We derive equations of motion for the looping pendulum using Newtonian mechanics, and show that these equations can be…
In the course of basic physics, more precisely the course of classical mechanics should be understood as clearly as possible the subject of rotational dynamics for students of science and engineering, to have clarity with the issues…
The motion of a classical pendulum in a gravitational field of strength g is explored. The complex trajectories as well as the real ones are determined. If g is taken to be imaginary, the Hamiltonian that describes the pendulum becomes…
This paper presents two novel approaches to solve the classic simple harmonic motion. In one approach, the distance between the equilibrium position and the maximal displacement is divided into N equal segments. In each segment, the mass…
The solutions that describe the motion of the classical simple pendulum have been known for very long time and are given in terms of elliptic functions, which are doubly periodic functions in the complex plane. The independent variable of…
The author considers the planar rotational motion of the mathematical pendulum with its pivot oscillating both vertically and horizontally, so the trajectory of the pivot is an ellipse close to a circle. The analysis is based on the exact…
This paper investigates the possibility of the motion control of a ball with a pendulum mechanism with non-holonomic constraints using gaits - the simplest motions such as acceleration and deceleration during the motion in a straight line,…
In the present paper, the nonlinear differential equation of pendulum is investigated to find an exact closed form solution, satisfying governing equation as well as initial conditions. The new concepts used in the suggested method are…