Final answer:
In each cycle, approximately 5.91% of the mechanical energy of a lightly damped oscillator is lost when its amplitude decreases by 3.0%. The closest provided answer choice is 6.0% (option b).
Step-by-step explanation:
The question pertains to the concept of damped harmonic motion in physics, specifically regarding how the amplitude decrease in a damped oscillator relates to mechanical energy loss. When the amplitude of a lightly damped oscillator decreases, it indicates that some of the mechanical energy of the system has been lost, typically due to non-conservative forces such as friction or air resistance. To calculate the percentage loss of mechanical energy when the amplitude decreases by 3.0%, one must understand that the energy of an oscillator is proportional to the square of its amplitude (E ≈ A^2).
If the amplitude decreases by 3.0%, the new amplitude becomes 97.0% of the original amplitude. Therefore, the new energy, being proportional to the square of the amplitude, becomes (0.97)^2 of the original energy, which calculates to approximately 94.09%. This means that 100% - 94.09% = 5.91% of the energy is lost in each cycle. Since this is not one of the provided options, we can approximate to the closest option which is 6.0%, answer choice (b).