We investigate the anharmonicity of a large amplitude pendulum and develop a novel technique to detect the high Fourier components as a function of the amplitude for large amplitudes close to 180°. The technique involves doing a Fourier analysis on each half-cycle of the amplitude versus time. The presence of the third and fifth harmonics is detected and the variations of the corresponding Fourier coefficients with amplitude are studied. The experimental setup is inexpensive and simple to implement.
Simple, simpler, simplest: Spontaneous pattern formation in a commonplace system Am. J. Phys. 80, 578 (2012) Determination of contact angle from the maximum height of enlarged drops on solid surfaces Am. J. Phys. 80, 284 (2012) Aerodynamics in the classroom and at the ball park Am. J. Phys. 80, 289 (2012) The added mass of a spherical projectile Am.The motion of a particle in different potentials is investigated theoretically and experimentally. The dependence of the period of oscillation on the amplitude is studied for pendula associated with some of these potentials. A technique is proposed to modify the trajectory of a pendulum bob so that it moves along a predetermined curve, and a simple and low cost experiment to study the relation between the period and amplitude for different potentials is discussed. We report on the motion of several pendula whose periods decrease with increasing amplitude. In particular, we study the effects of a perturbation of the form z 4 on the frequency of oscillation of a simple harmonic oscillator. Our results agree with the expectation that any perturbation of a simple harmonic oscillator destroys its isochronism.
We experimentally studied the dependence of the period of the interrupted pendulum as a function of the amplitude for small angles of oscillation. We found a new kind of dependence of the period with the amplitude of the pendulum that indicates that if the interruption is not located on the main vertical axis that contains the point of suspension, the period of the interrupted pendulum is highly nonisochronous and does not converge to a definite value as the maximum amplitude approaches zero. We have developed a simple model that satisfactorily explains the experimental data with no adjustable parameters. This property of the interrupted pendulum is a general property of the parabolic potential consisting of two quadratic forms with different curvatures that join at a point different from the apex or the vertex.
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