In order to test SHM, the behaviour changes of a torsion pendulum due to different damping factors as well as its changes due to applying an external exciter were observed and compared with the theoretical expectations. The quality factor of the same damping state (with a brake current of 6A in the eddy brakes) was calculated using two different approaches and the resulting values were found to be within ơ of each one, as Q1 = 6.0±1.3 and Q2 = 7.5±0.7. The first approach was based on measuring the maximum displacement for each successive oscillation and deducing the slope from the plot of the natural logarithm of the amplitude against the number of oscillations. Differently, the second estimate of Q was obtained under forced oscillation conditions by taking the ratio of the experimentally determined resonance amplitude and the amplitude of natural oscillation.
Table of Contents
- Introduction
- Theoretical Background
- Methods and Results
- Discussion
- Conclusion
Objectives and Key Themes
The experiment aims to investigate free, damped, and forced simple harmonic motion (SHM) in a torsional pendulum. By analyzing the behavior of the pendulum under different damping conditions, the experiment aims to determine the quality factor Q and the resonance frequency. Additionally, it aims to explore how damping affects the amplitude of the response to a sinusoidal driving force.
- Damped Oscillations and the Quality Factor Q
- Forced Oscillations and Resonance Phenomena
- Influence of Damping on Amplitude Response
- Torsional Pendulum as a Model System
- Applications of Torsional Pendulums in Research
Chapter Summaries
- Introduction: This chapter introduces the experiment's objective, which is to study free, damped, and forced SHM in a torsional pendulum. It also highlights the importance of determining the quality factor Q and resonance frequency.
- Theoretical Background: This chapter provides a theoretical foundation for understanding SHM, particularly focusing on the damped and forced oscillations of a torsional pendulum. It introduces key concepts such as the restoring torque, the decay constant, and the amplitude resonant frequency.
- Methods and Results: This chapter describes the experimental setup and procedures used to study the transient and forced responses of the torsional pendulum. It presents the results of the measurements, including the determination of the quality factor Q and the resonance frequency.
Keywords
The key terms and concepts central to this text are: torsional pendulum, simple harmonic motion (SHM), damped oscillations, forced oscillations, quality factor Q, resonance frequency, eddy current brake, amplitude, decay constant, natural frequency, transient response, steady-state response, and the equivalence principle.
- Quote paper
- Laura Imperatori (Author), 2012, Mechanical Resonance. Free and forced SHM of a torsional pendulum, Munich, GRIN Verlag, https://www.grin.com/document/268472
