Resonance- Circuit and Mechanical

In summary, the conversation discusses the analogy between mechanical oscillations and AC circuits. It is noted that for a mass on a spring, resonance occurs at a phase difference of 90 degrees, while for a series RLC circuit, resonance occurs at a phase difference of 0 degrees. The conversation then questions why the analogy breaks down at this point and compares how the driving force is applied in both systems. It is concluded that the analogy breaks down because displacement corresponds to charge and current corresponds to velocity, leading to the 90 degree difference.
  • #1
StandardBasis
22
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I am studying the analogy between mechanical oscillations and AC circuits.

For a mass on a spring, resonance occurs when there is a phase difference of 90 degrees. It seems like for a series RLC circuit, resonance must occur at a phase different of 0 degrees between the voltage from the source and the current (because inductive and capacitive reactances cancel).

Why does the analogy break down there?
 
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  • #2
For mass on a spring - where is the driving force applied?
Compare with how the driving force is applied in a RCL circuit.
 
  • #3
If you look at the differential equations for mechanical and electrical oscillations, the analogy is that displacement corresponds to charge, not to current.

Current corresponds to velocity in the mechanical system, not to displacement. That's where the "90 degrees difference" comes from.
 

Related to Resonance- Circuit and Mechanical

What is resonance?

Resonance is a phenomenon that occurs when an object or system is subjected to a periodic force or vibration at its natural frequency, causing it to oscillate with maximum amplitude.

What is a resonant circuit?

A resonant circuit is an electrical circuit that contains an inductor and a capacitor, which can store and release energy at specific frequencies. It exhibits resonance behavior when the frequency of the input signal matches the natural frequency of the circuit.

How does resonance affect mechanical systems?

In mechanical systems, resonance can cause excessive vibrations and stress on components, potentially leading to equipment failure. However, it can also be harnessed for useful applications, such as in musical instruments.

How does resonance impact sound and music?

Resonance plays a crucial role in sound and music. In musical instruments, resonance helps to amplify and sustain specific frequencies, creating harmonious tones. In sound systems, resonance can cause unwanted feedback and distortion if not properly controlled.

What are some real-world examples of resonance?

Some common examples of resonance include a swing in a playground, a tuning fork, and a guitar string. In engineering, resonance can be seen in bridges and buildings that sway during strong winds. In chemistry, resonance is used to explain the structure of molecules.

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