Question Detail
Question
The time constant τ for a damped oscillator is related to the decay of energy E(t) = E₀e-t/τ. After one time constant (t = τ), what is the energy relative to the initial energy E₀?
Correct Answer
Option B is the correct answer.
Detailed Explanation
From Equation (51) on page 22, the energy is given by E(t) = E₀e-t/τ. Substituting t = τ yields E(τ) = E₀e-τ/τ = E₀e-1 = E₀/e.
Hint
Recall the definition of the natural exponential function and what happens when the exponent is -1.