A damped oscillator has a decay time constant $\tau$.After time t = $\tau$ has passed,the fraction of the amount of energy remaining is
A)0.25
B)0.37
C)0.5
D)0.67
E)0.75

Question

Quizplus · Accepted Answer

The fraction of energy remaining after time t is given by:

E(t) = E(0) * e^(-t/tau)

where E(0) is the initial energy, tau is the decay time constant, and t is the time elapsed.

If t = tau, then:

E(tau) = E(0) * e^(-tau/tau) = E(0) * e^(-1) ≈ 0.37 E(0)

Therefore, after a time of t = tau has passed, the fraction of the amount of energy remaining is approximately 0.37 or 37% of the initial energy. Hence, the correct answer is B.

A Damped Oscillator Has a Decay Time Constant τ\tauτ After Time T =

A Damped Oscillator Has a Decay Time Constant $\tau$ After Time T =