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The amplitude of a damped oscillator decreases to 0.9 times its original magnitude in 5s. In another 10s it will decrease to α times its original magnitude, where α equals
- 0.7
- 0.729
- 0.81
- 0.6
Correct answer: 0.729
Solution
The amplitude of a damped oscillator decreases exponentially over time. Given that it decreases to 0.9 of its original value in 5 seconds, we can use the exponential decay formula to find the amplitude after an additional 10 seconds, resulting in a decrease to approximately 0.729 of its original magnitude.
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