Analysis of a simple pendulum driven at its suspension point

European Journal of Physics

The resonance characteristics of a driven damped harmonic oscillator are well known. Unlike harmonic oscillators which are guided by parabolic potentials, a simple pendulum oscillates under sinusoidal potentials. The problem of an undamped pendulum has been investigated to a great extent. However, the resonance characteristics of a driven damped pendulum have not been reported so far due to the difficulty in solving the problem analytically. In the present work we report the resonance characteristics of a driven damped pendulum calculated numerically. The results are compared with the resonance characteristics of a damped driven harmonic oscillator. The work can be of pedagogic interest too as it reveals the richness of driven damped motion of a simple pendulum in comparison to and how strikingly it differs from the motion of a driven damped harmonic oscillator. We confine our work only to the nonchaotic regime of pendulum motion.

arXiv: Classical Physics, 2019

The characteristics of drive-free oscillations of a damped simple pendulum under sinusoidal potential force field differ from those of the damped harmonic oscillations. The frequency of oscillation of a large amplitude simple pendulum decreases with increasing amplitude. Many prototype mechanical simple pendulum have been fabricated with precision and studied earlier in view of introducing them in undergraduate physics laboratories. However, fabrication and maintenance of such mechanical pendulum require special skill. In this work, we set up an analog electronic simulation experiment to serve the purpose of studying the force-free oscillations of a damped simple pendulum. We present the details of the setup and some typical results of our experiment. The experiment is simple enough to implement in undergraduate physics laboratories.

Physics Letters A, 1994

A phenomenological equation of motion is proposed to account for two distinctive features of low-frequency inverted pendulums: frequency independent internal losses and instability at resonance frequencies below a critical threshold. The comparison with recent experimental data is discussed in detail. A new characterization of the background loss for a mass suspended as a pendulum by wires is also derived.

International Journal of Interactive Mobile Technologies (iJIM)

During pendulum analysis, the approximation for small angles is usually performed as a simple harmonic motion. However, for large angles, this approximation is not convenient so exact solutions are proposed by differ-ent methods. This paper presents the comparison of two solutions for the displacement of the pendulum in the domain of time and frequency, the solution by Jacobi elliptic function and the solution by the numerical method Dormand-Prince with the results of measurements obtained by means of a physical prototype designed for the teaching of physics. We consider that this comparative study allows a better understanding of the phenomenon of the non-linear pendulum in the students of undergraduate careers in the physics of waves as well as a previous training for the course of analysis of signals being in good exercise of teaching

International Applied Mechanics, 1977

The aim of the present article is an approximate investigation of the effect of two mechanisms of the generation of vibrations -parametric and autooscillational -on the formation of the resonant states of a physical pendulum with friction at its axis, for vibration of this axis. Certain problems in the dynamics of mechanisms with elastic connections, working under conditions of the vibration of the base or pulsation of an external force, problems of the vibrations of scales, a number of problems of determination of the dynamic accuracy of measuring instruments, etc., can be brought down to the study of such a mechanical model. Investigation of the dynamics of the system under consideration is also of independent interest, since, using a relatively simple example, it permits following the principal special characteristics of the dynamic interaction of the mechanisms for the generation of vibrations most used in practice, i.e., parametric, autooscillationa[, and an external harmonic force.

2006

Experiments on the oscillatory motion of a suspended bar magnet throws light on the damping effects acting on the pendulum. The viscous drag offered by air was found the be the main contributor for slowing the pendulum down. The nature and magnitude of the damping effects were shown to be strongly dependent on the amplitude.

In our discussion of the damped pendulum case we have dealt with two different types of damping,

Journal of Sound and Vibration, 2012

Meccanica

We propose a general model for pendular systems with an arbitrary number of links arranged sequentially. The form of this model is easily adaptable to different settings and operating conditions. The main subject of analysis is a system obtained as a specific case taken from the general analysis, a three-links pendulum with damping subject to periodic perturbation. We performed a theoretical analysis of the frequency response and compared it with results from temporal integration. Moreover, a law was obtained explaining the behavior of the shift of the resonant frequencies due to a change in a parameter.

European Journal of Physics, 1999

Damped oscillatory motion is one of the most widely studied movements in physics courses. Despite this fact, dry damped oscillatory motion is not commonly discussed in physics textbooks. In this work, we discuss the dry and viscous damped pendulum, in a teaching experiment that can easily be performed by physics or engineering students.