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If 
is the natural frequency of the system and 
is the frequency of the external force that acts on an oscillating system then at resonance
is the natural frequency of the system and is the frequency of the external force that acts on an oscillating system then at resonance- a)ωd ≥ ω
- b)ωd = ω
- c)ωd ≤ ω
- d)ωd ≠ ω
Correct answer is option 'B'. Can you explain this answer?
Most Upvoted Answer
Ifis the natural frequency of the system andis the frequency of the ex...
When the natural frequency and external frequency of an object are equal the phenomenon is called resonance.
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Ifis the natural frequency of the system andis the frequency of the ex...
Resonance in Oscillating Systems
Resonance occurs in oscillating systems when the frequency of the external force matches the natural frequency of the system. Here's a detailed explanation:
Natural Frequency (ω)
- The natural frequency (ω) is the frequency at which a system tends to oscillate in the absence of any external force.
- Every oscillating system, such as a pendulum or a spring-mass system, has a specific natural frequency determined by its physical properties.
Driving Frequency (ωd)
- The driving frequency (ωd) is the frequency of the external force applied to the system.
- This force can come from various sources, such as motors, vibrations, or periodic inputs.
Condition for Resonance
- Resonance occurs when the driving frequency equals the natural frequency of the system, i.e., ωd = ω.
- At this point, the system absorbs maximum energy from the driving force, leading to large amplitude oscillations.
Why Option B is Correct
- The question states that at resonance, the condition is ωd = ω.
- This means the external force frequency must match the system's natural frequency for resonance to occur.
- Consequently, options a, c, and d are incorrect as they suggest different relationships between ωd and ω.
Conclusion
- Understanding resonance is crucial in fields like engineering, music, and physics, as it plays a significant role in the stability and efficiency of oscillating systems.
By recognizing this relationship, one can predict and harness the effects of resonance effectively.
Resonance occurs in oscillating systems when the frequency of the external force matches the natural frequency of the system. Here's a detailed explanation:
Natural Frequency (ω)
- The natural frequency (ω) is the frequency at which a system tends to oscillate in the absence of any external force.
- Every oscillating system, such as a pendulum or a spring-mass system, has a specific natural frequency determined by its physical properties.
Driving Frequency (ωd)
- The driving frequency (ωd) is the frequency of the external force applied to the system.
- This force can come from various sources, such as motors, vibrations, or periodic inputs.
Condition for Resonance
- Resonance occurs when the driving frequency equals the natural frequency of the system, i.e., ωd = ω.
- At this point, the system absorbs maximum energy from the driving force, leading to large amplitude oscillations.
Why Option B is Correct
- The question states that at resonance, the condition is ωd = ω.
- This means the external force frequency must match the system's natural frequency for resonance to occur.
- Consequently, options a, c, and d are incorrect as they suggest different relationships between ωd and ω.
Conclusion
- Understanding resonance is crucial in fields like engineering, music, and physics, as it plays a significant role in the stability and efficiency of oscillating systems.
By recognizing this relationship, one can predict and harness the effects of resonance effectively.
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Ifis the natural frequency of the system andis the frequency of the external force that acts on an oscillating system then at resonancea)ωd≥ωb)ωd=ωc)ωd≤ωd)ωd≠ωCorrect answer is option 'B'. Can you explain this answer? for Class 11 2025 is part of Class 11 preparation. The Question and answers have been prepared according to the Class 11 exam syllabus. Information about Ifis the natural frequency of the system andis the frequency of the external force that acts on an oscillating system then at resonancea)ωd≥ωb)ωd=ωc)ωd≤ωd)ωd≠ωCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for Class 11 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Ifis the natural frequency of the system andis the frequency of the external force that acts on an oscillating system then at resonancea)ωd≥ωb)ωd=ωc)ωd≤ωd)ωd≠ωCorrect answer is option 'B'. Can you explain this answer?.
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