In a damped harmonic oscillator, the mechanical energy decreases by 10% in each full cycle. After 3 complete cycles, what percentage of the initial energy remains?
Answer and explanation
Correct answer: A. 72.9%
- Step 1: After 1 cycle, remaining energy fraction is 1 - 0.10 = 0.90.
- Step 2: After 3 cycles, remaining energy is E_3 = E_0 * (0.90)^3.
- Step 3: Calculate: (0.9)^3 = 0.729.
- Step 4: In percentage, this is 72.9%.
Answer
72.9%.
Why not the others: 70.0% assumes linear loss (100% - 3 * 10%); 81.0% is after 2 cycles; 65.6% is (0.9)^4 (after 4 cycles).
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