Final answer:
To find the time constant of a damped oscillator that decreases to 36.8% of its initial energy in 10.0 seconds, we use the decay formula and solve for the time constant, yielding a value just over 5 seconds. The closest provided answer is E. 5.0 sec.
Step-by-step explanation:
The student is asking about the time constant of a damped oscillator that decreases its energy to 36.8% of its initial value in 10.0 seconds. The time constant (τ) can be found using the property that the energy (E) of a damped oscillator decreases according to the equation E = E0e−t/τ, where E0 is the initial energy, t is the time, and τ is the time constant.
Solving for τ using the given information (E/E0 = 0.368 and t = 10.0s), we find that τ ≈ 10.0s / ln(1/0.368), resulting in a time constant just over 5 seconds. The closest answer provided is E. 5.0 sec.