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Chapter 13: Problem 15

How can a system have more than one resonant frequency?

Short Answer

Expert verified
A system can have more than one resonant frequency due to the presence of multiple components or parts, each of which could potentially have its own unique natural frequency. When these components are subjected to an external stimulus of a frequency equal to their natural frequencies, they each resonate, leading to multiple resonant frequencies for the entire system.

Step by step solution

01

Understanding Resonance

Resonance is a phenomenon that occurs when an object or system is driven to oscillate at specific frequencies, called resonant frequencies. These are the frequencies at which the system naturally tends to vibrate. When an external stimulus of a frequency equal to the system's natural frequency is applied to the system, the system resonates and its amplitude of oscillation increases dramatically.
02

Complexity of Systems

When we think about complex systems such as an electrical circuit or a mechanical system with many components, there isn't just one natural frequency. Each component, such as an inductor, a capacitor in an electrical circuit, or a spring in a mechanical system, can have its own natural frequency. Therefore, when an external stimulus is applied, each component vibrates at its intrinsic frequency if the conditions allow.
03

Multiple Resonant Frequencies

As a result of different components having different natural frequencies, a system can have more than one resonant frequency. For instance, in an electrical circuit with multiple LC circuits (consisting of an inductor and capacitor), each LC circuit can resonate at a different frequency. The resonant frequencies of a system are the natural frequencies of the individual components that make up the system. Therefore, a system with numerous different components with differing natural frequencies will produce multiple resonant frequencies when the appropriate external stimuli are applied.

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