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Sharpness of resonance is
- a)directly proportional to damping force
- b)inversely proportional to damping force
- c)equal to square of damping force
- d)None of the above
Correct answer is option 'B'. Can you explain this answer?
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Sharpness of resonance isa)directly proportional to damping forceb)inv...
Sharpness of resonance
Resonance is a phenomenon that occurs when a system is driven by an external force at its natural frequency. This results in a large amplitude response in the system. The sharpness of resonance refers to how narrow or wide the resonance peak is in a frequency response curve.
Inversely proportional to damping force
The sharpness of resonance is inversely proportional to the damping force. Damping is a force that opposes the motion of a vibrating system, and it is responsible for dissipating energy from the system. The damping force can be described as the resistance encountered by the system as it moves through a medium.
How damping affects resonance
Damping affects resonance by reducing the amplitude of the response. It does this by dissipating energy from the system, which results in a decrease in the peak amplitude of the resonance curve. The greater the damping force, the more energy is dissipated, and the less sharp the resonance peak becomes.
Explanation
When a system is underdamped (has low damping), the resonance peak is sharp. This means that the amplitude of the response is very large at the resonant frequency and quickly drops off as the frequency moves away from the resonant frequency. In an underdamped system, there is not much energy dissipation, so the system can vibrate with a large amplitude.
On the other hand, when a system is overdamped (has high damping), the resonance peak is wide. This means that the amplitude of the response is still large at the resonant frequency, but it decreases more gradually as the frequency moves away from the resonant frequency. In an overdamped system, there is significant energy dissipation, so the system cannot vibrate with a large amplitude.
Conclusion
In summary, the sharpness of resonance is inversely proportional to the damping force. A higher damping force leads to a wider resonance peak, while a lower damping force leads to a sharper resonance peak. This relationship is important in understanding the behavior of vibrating systems and their response to external forces.
Resonance is a phenomenon that occurs when a system is driven by an external force at its natural frequency. This results in a large amplitude response in the system. The sharpness of resonance refers to how narrow or wide the resonance peak is in a frequency response curve.
Inversely proportional to damping force
The sharpness of resonance is inversely proportional to the damping force. Damping is a force that opposes the motion of a vibrating system, and it is responsible for dissipating energy from the system. The damping force can be described as the resistance encountered by the system as it moves through a medium.
How damping affects resonance
Damping affects resonance by reducing the amplitude of the response. It does this by dissipating energy from the system, which results in a decrease in the peak amplitude of the resonance curve. The greater the damping force, the more energy is dissipated, and the less sharp the resonance peak becomes.
Explanation
When a system is underdamped (has low damping), the resonance peak is sharp. This means that the amplitude of the response is very large at the resonant frequency and quickly drops off as the frequency moves away from the resonant frequency. In an underdamped system, there is not much energy dissipation, so the system can vibrate with a large amplitude.
On the other hand, when a system is overdamped (has high damping), the resonance peak is wide. This means that the amplitude of the response is still large at the resonant frequency, but it decreases more gradually as the frequency moves away from the resonant frequency. In an overdamped system, there is significant energy dissipation, so the system cannot vibrate with a large amplitude.
Conclusion
In summary, the sharpness of resonance is inversely proportional to the damping force. A higher damping force leads to a wider resonance peak, while a lower damping force leads to a sharper resonance peak. This relationship is important in understanding the behavior of vibrating systems and their response to external forces.
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Sharpness of resonance isa)directly proportional to damping forceb)inversely proportional to damping forcec)equal to square of damping forced)None of the aboveCorrect answer is option 'B'. Can you explain this answer?
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