Welcome to the article Determine whether the following statement is true or false The size of oscillations of the undamped forced harmonic oscillator increases without bound in the resonance. On this page, you will learn the essential and logical steps to better understand the topic being discussed. We hope the information provided helps you gain valuable insights and is easy to follow. Let’s begin the discussion!
Answer :
Final answer:
True, in the resonance case for an undamped, forced harmonic oscillator, the amplitude of oscillations increases without bound because no energy is dissipated. Real-world systems often have some damping, which prevents infinite growth of amplitude.
Explanation:
The statement that the size of oscillations of the undamped, forced harmonic oscillator increases without bound in the resonance case is True. When a harmonic oscillator is driven by a periodic force at its natural frequency without damping, the phenomenon of resonance occurs. Without any damping to dissipate energy, the amplitude of oscillation will indeed increase with time, making the system more and more energetic as it continues to absorb energy from the driving force at the natural frequency. This can lead to infinitely large oscillations if no non-conservative forces are present to remove energy from the system.
It's important to note that in real-world situations, some form of damping usually exists, which prevents the amplitude from increasing without bound by dissipating energy. As such, figures like Figure 16.22, which show the amplitude decreasing over time, reflect systems with some damping. Figures 16.25 and 16.27 detail how the amplitude response of harmonic oscillators varies with the frequency of the driving force and highlight that resonance leads to a peak amplitude when the driving frequency matches the natural frequency of the system, especially when damping is minimal.
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Rewritten by : Brahmana