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Assertion: In the ideal case of zero dam...

Assertion: In the ideal case of zero damping, the amplitude of simpl harmonic motion at resonance is is infinite.
Reason: All real sysmtems have some damping.

A

If both assertion and reson are true and reason is the correct explanation of assertion

B

If both assertion and reason are true but reason is not the correct explanation of assertion.

C

If assertion is true but reason is false.

D

If both assertion and reason are false.

Text Solution

AI Generated Solution

The correct Answer is:
To solve the assertion and reason question, we will analyze both statements step by step. ### Step 1: Analyze the Assertion The assertion states that "In the ideal case of zero damping, the amplitude of simple harmonic motion at resonance is infinite." - In a system undergoing simple harmonic motion (SHM), resonance occurs when the frequency of an external force matches the natural frequency of the system. - In the absence of damping (ideal case), the energy supplied to the system can continuously increase the amplitude of oscillation. - As a result, theoretically, if damping is zero, the amplitude can grow indefinitely, leading to the conclusion that the amplitude at resonance would indeed be infinite. **Conclusion for Assertion:** True ### Step 2: Analyze the Reason The reason states that "All real systems have some damping." - In reality, every physical system experiences some form of damping due to factors like friction, air resistance, or internal material properties. - Damping acts to dissipate energy from the system, which prevents the amplitude from becoming infinite. - Therefore, this statement is also true as it reflects the behavior of real-world systems. **Conclusion for Reason:** True ### Step 3: Determine the Relationship Between Assertion and Reason Now, we need to determine if the reason provided correctly explains the assertion. - While both statements are true, the reason does not explain why the assertion is true. The assertion talks about an ideal case (zero damping) leading to infinite amplitude, while the reason discusses the reality of damping in all systems. - Thus, the reason does not provide a correct explanation for the assertion. ### Final Conclusion The correct option is that both the assertion and reason are true, but the reason is not the correct explanation of the assertion. ### Summary of the Solution: - Assertion: True (in zero damping, amplitude at resonance is infinite) - Reason: True (all real systems have some damping) - Relationship: Reason does not explain the assertion.
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