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

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.