A: In a forced oscillator the energy transferred from driving force to damped oscillator is maximum in resonance state.
R: The amplitude of forced oscillator depends on the frequency of external force.

Options

A. If both Assertion & Reason are true and the reason is the correct explanation of the assertion, then mark (1)
B. If both Assertion & Reason are true but the reason is not the correct explanation of the assertion, then mark (2)
C. If Assertion is true statement but Reason is false then mark (3)
D. If both Assertion and Reason are false statements, then mark (4)

Answer

To analyze the statements provided in the question, we need to evaluate both statement A and statement R.

### Step 1: Understand Statement A
Statement A claims that in a forced oscillator, the energy transferred from the driving force to the damped oscillator is maximum in the resonance state.

- **Resonance** occurs when the frequency of the external driving force matches the natural frequency of the oscillator. At this point, the system can absorb energy most efficiently from the driving force, leading to maximum amplitude of oscillation.
- In a damped oscillator, energy is lost due to damping forces (like friction), but at resonance, the energy supplied by the driving force can compensate for this loss, resulting in maximum energy transfer.

**Conclusion for A**: Statement A is true.

### Step 2: Understand Statement R
Statement R states that the amplitude of the forced oscillator depends on the frequency of the external force.

- The amplitude of a forced oscillator indeed varies with the frequency of the external force. When the frequency of the driving force is close to the natural frequency of the oscillator, the amplitude increases significantly. Conversely, if the frequency is far from the natural frequency, the amplitude is lower.
- This relationship is crucial in understanding how oscillators behave under different driving frequencies.

**Conclusion for R**: Statement R is also true.

### Step 3: Determine the Relationship between A and R
Both statements A and R are true, and statement A provides a specific condition (resonance) under which the energy transfer is maximized, while statement R describes a general relationship between amplitude and driving frequency.

### Final Conclusion
Both statements A and R are true, and R explains a fundamental characteristic of forced oscillators that supports the assertion made in A.

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