skip to main content
US FlagAn official website of the United States government
dot gov icon
Official websites use .gov
A .gov website belongs to an official government organization in the United States.
https lock icon
Secure .gov websites use HTTPS
A lock ( lock ) or https:// means you've safely connected to the .gov website. Share sensitive information only on official, secure websites.

Attention:

The NSF Public Access Repository (PAR) system and access will be unavailable from 10:00 PM ET on Friday, February 6 until 10:00 AM ET on Saturday, February 7 due to maintenance. We apologize for the inconvenience.

Explore Research Products in the PAR
It may take a few hours for recently added research products to appear in PAR search results.


Title: Does a physical pendulum ever act like a simple pendulum?
Abstract We show that for a physical pendulum comprising a massive sphere swinging from a massive string, there is, in general, a length of string for which its oscillatory period equals the period calculated by the simple pendulum model with a point-like mass swinging from a massless string whose model length equals the summed length of the real string and the sphere’s radius.  more » « less
Award ID(s):
2110358
PAR ID:
10530304
Author(s) / Creator(s):
;
Publisher / Repository:
IOP
Date Published:
Journal Name:
European Journal of Physics
Volume:
45
Issue:
2
ISSN:
0143-0807
Page Range / eLocation ID:
025001
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
More Like this
  1. ; ; (, Complex Light and Optical Forces XVI, 1201704)
    Andrews, David L.; Galvez, Enrique J.; Rubinsztein-Dunlop, Halina (Ed.)
    The similarity between the 2D Helmholtz equation in elliptical coordinates and the Schr¨odinger equation for the simple mechanical pendulum inspires us to use light to mimic this quantum system. When optical beams are prepared in Mathieu modes, their intensity in the Fourier plane is proportional to the quantum mechanical probability for the pendulum. Previous works have produced a two-dimensional pendulum beam that oscillates as a function of time through the superpositions of Mathieu modes with phases proportional to pendulum energies. Here we create a three-dimensional pendulum wavepacket made of a superposition of Helical Mathieu-Gaussian modes, prepared in such a way that the components of the wave-vectors along the propagation direction are proportional to the pendulum energies. The resulting pattern oscillates or rotates as it propagates, in 3D, with the propagation coordinate playing the role of time. We obtained several different propagating beam patterns for the unbound-rotor and the bound-swinging pendulum cases. We measured the beam intensity as a function of the propagation distance. The integrated beam intensity along elliptical angles plays the role of quantum pendulum probabilities. Our measurements are in excellent agreement with numerical simulations. 
    more » « less
  2. ; ; ; (, Nonlinear Dynamics)
    Abstract This article studies the nonreciprocity of a system that consists of a bistable element coupled to a monostable element through a contactless magnetic interaction. To illustrate the concept, the bistable element is physically realized using a pendulum that interacts with a stationary magnet and the monostable element is a classical pendulum. A numerical model is implemented to simulate the nonlinear dynamics of the system. Both simulations and experiments show that the system exhibits a strong amplitude-dependent nonreciprocity in response to initial excitations. At small input amplitudes, the system has an intrawell response with minimal transmission of energy whether the excitation is exerted on the side of the bistable pendulum or on the other side. However, at high input amplitude, a strong nonreciprocal behavior is observed: excitation of the bistable pendulum causes an interwell response which considerably reduces the distance between the two pendulums and allows energy to be efficiently transmitted through the contactless magnetic interaction; excitation of the monostable pendulum does not cause any interwell response and results in limited energy transmission. The combination of bistability and contactless nonlinear interactions allows the system to exhibit very strong amplitude-dependent nonreciprocity, which may be useful in a wide range of applications. 
    more » « less
  3. ; (, 2022 ASME IDETC conference (American Society of Mechanical Engineers, International Design Engineering Technical Conferences))
    Abstract A nonlinear inerter pendulum vibration absorber is integrated with an electromagnetic power take-off system (called IPVA-PTO) and is analyzed for its efficacy in ocean wave energy conversion of a spar platform. The IPVA-PTO system shows a nonlinear energy transfer phenomenon between the spar and the IPVA-PTO which can be used to convert the vibration energy of the spar into electricity while reducing the hydrodynamic response of the spar. The hydrodynamic coefficients of the spar are computed using a commercial boundary-element-method (BEM) code. It is shown that the energy transfer is associated with 1:2 internal resonance of the pendulum vibration absorber, which is induced by a period-doubling bifurcation. The period-doubling bifurcation is studied using the harmonic balance method. A modified alternating frequency/time (AFT) approach is developed to compute the Jacobian matrix involving nonlinear inertial effects of the IPVA-PTO system. It is shown that the period-doubling bifurcation leads to 1:2 internal resonance and plays a major role in the energy transfer between the spar and the pendulum. The response amplitude operator (RAO) in heave and the capture width of the IPVA-PTO-integrated spar are compared with its linear counterpart and it is shown that the IPVA-PTO system outperforms the linear energy harvester as the former has a lower RAO and higher capture width. 
    more » « less
  4. ; (, Journal of Vibration and Acoustics)
    Abstract The inerter has been integrated into various vibration mitigation devices, whose mass amplification effect could enhance the suppression capabilities of these devices. In the current study, the inerter is integrated with a pendulum vibration absorber, referred to as inerter pendulum vibration absorber (IPVA). To demonstrate its efficacy, the IPVA is integrated with a linear, harmonically forced oscillator seeking vibration mitigation. A theoretical investigation is conducted to understand the nonlinear response of the IPVA. It is shown that the IPVA operates based on a nonlinear energy transfer phenomenon wherein the energy of the linear oscillator transfers to the pendulum vibration absorber as a result of parametric resonance of the pendulum. The parametric instability is predicted by the harmonic balance method along with the Floquet theory. A perturbation analysis shows that a pitchfork bifurcation and period doubling bifurcation are necessary and sufficient conditions for the parametric resonance to occur. An arc-length continuation scheme is used to predict the boundary of parametric instability in the parameter space and verify the perturbation analysis. The effects of various system parameters on the parametric instability are examined. Finally, the IPVA is compared with a linear benchmark and an autoparametric vibration absorber and shows more efficacious vibration suppression. 
    more » « less
  5. ; ; (, Journal of Vibration and Acoustics)
    Abstract The inerter pendulum vibration absorber (IPVA) is integrated between a spar and an annulus floater using a ball-screw mechanism to study its wave energy conversion potential. Hydrodynamic stiffness, added mass, and radiation damping effects on the spar-floater system are characterized using the boundary element method. It is found that a 1:2 internal resonance via a period-doubling bifurcation in the system is responsible for nonlinear energy transfer between the spar-floater system and the pendulum vibration absorber. This nonlinear energy transfer occurs when the primary harmonic solution of the system becomes unstable due to the 1:2 internal resonance phenomenon. The focus of this paper is to analyze this 1:2 internal resonance phenomenon near the first natural frequency of the system. The IPVA system when integrated with the spar-floater system is shown to outperform a linear coupling between the spar and the floater both in terms of the response amplitude operator (RAO) of the spar and one measure of the energy conversion potential of the system. Finally, experiments are performed on the IPVA system integrated with single-degree-of-freedom system (without any hydrodynamic effects) to observe the 1:2 internal resonance phenomenon and the nonlinear energy transfer between the primary mass and the pendulum vibration absorber. It is shown experimentally that the IPVA system outperforms a linear benchmark in terms of vibration suppression due to the energy transfer phenomenon. 
    more » « less
  • Citation Formats
  • MLA
  • APA
  • Chicago
  • BibTeX
  • Text Encoded Conversion
  • XML
  • Save / Share this Record
  • Send to Email