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Longitudinal oscillations and flights of the string pendulum driven by a periodic force
1Department of Mechanical Engineering, Technion-Israel Institute of Technology, Haifa 32000, Israel.
Summary
String pendulum oscillations involve harmonic motion and free flights under gravity. A resonance mechanism amplifies flight amplitude, driven by free oscillations, with resonance frequency matching the string
Area of Science:
- Physics
- Mechanical Engineering
- Oscillations and Waves
Background:
- String pendulums exhibit complex dynamics beyond simple harmonic motion.
- Understanding energy transfer and amplitude amplification is crucial for analyzing such systems.
Purpose of the Study:
- To investigate the longitudinal oscillations of a string pendulum.
- To analyze the free flight regime and its impact on overall motion.
- To describe the resonance phenomenon and its underlying mechanism.
Main Methods:
- Theoretical analysis of pendulum motion under gravity and elastic forces.
- Identification of the conditions leading to free flight phases.
- Mathematical description of the resonance phenomenon and energy transfer.
Main Results:
- The string pendulum exhibits two types of motion: harmonic oscillations and free flights under gravity.
- Free flights can lead to significant amplitude amplification, exceeding forced oscillation amplitudes.
- A resonance mechanism is identified where free oscillations pump energy into the system.
Conclusions:
- The resonance frequency is equal to the fundamental frequency of the string.
- Resonance amplitude is proportional to the square of the regular forced oscillation amplitude.
- This study reveals a novel mechanism for amplitude amplification in string pendulums.
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