Welcome to the article The external input s frequency at which a second order system produces its largest possible response is when practical resonance occurs True False. 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 :
True, a second order system has its largest response at the frequency of practical resonance, which is typically when the driving force's frequency matches the natural frequency of the system.
The statement that a second order system produces its largest possible response at the frequency of practical resonance is True. A vibrating system does resonate at its own natural frequency, which means that the system exhibits maximum amplitude when the frequency of the external driving force matches the system's natural frequency. However, it is important to note that, technically, the maximum amplitude can occur at a frequency slightly different from the natural frequency due to the influence of damping forces, but for many practical purposes, the largest response is still associated with the natural frequency.
When the driving force frequency is equal to the natural frequency of the system, as mentioned in Statement 2, the amplitude of the steady-state response is greatest. This phenomenon is known as resonance. The equation provided also depicts that at the frequency () close to the natural frequency (o), the amplitude ( ext{A}) is maximized, which corresponds with the intuitive and empirical observations of resonant behavior.
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