What is the time constant of an oscillator if its amplitude of oscillation is decreased to 27.9% of its original value in 9.70 s? 7.60 s 1.46 s 15.2 s 3.80 s
Question
What is the time constant of an oscillator if its amplitude of oscillation is decreased to 27.9% of its original value in 9.70 s? 7.60 s 1.46 s 15.2 s 3.80 s
Solution
The time constant of an oscillator is defined as the time it takes for the amplitude of oscillation to decrease to 36.8% (or 1/e) of its original value.
Given that the amplitude of oscillation decreased to 27.9% in 9.70 seconds, we can use the formula for exponential decay to find the time constant. The formula is:
A = A0 * e^(-t/τ)
where: A is the final amplitude (27.9% of the original), A0 is the initial amplitude (100%), t is the time (9.70 seconds), and τ is the time constant we're trying to find.
Rearranging the formula to solve for τ gives:
τ = -t / ln(A/A0)
Substituting the given values gives:
τ = -9.70 / ln(0.279)
Calculating this gives a time constant of approximately 7.60 seconds. So, the correct answer is 7.60 s.
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