Question Detail

PHY 104 Oscillatory Motion Objective Question
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Question

In damped oscillations, the time constant τ is defined as m/b (where b is the damping constant and m is mass). How is the time constant τ related to the energy decrease of the system?
Options
A It is the time for the amplitude to decrease by a factor of 1/e.
B It is the time for the energy to decrease by a factor of 1/e.
Correct Answer
C It is the time for the energy to decrease by a factor of 1/2.
D It is the time for the amplitude to decrease to zero.
Correct Answer

Option B is the correct answer.

Detailed Explanation

Page 22 states that the amplitude decreases as A(t) = A_0 e^(-t/2τ) and the energy decreases as E(t) = E_0 e^(-t/τ). Therefore, τ is the time for the energy to decrease by a factor of 1/e.

Hint

Recall the exponential decay formulas for amplitude and energy in damped oscillations.

Question Info

Course: PHY 104
Topic: Oscillatory Motion
Type: Objective
Difficulty: Not specified
Question 285 of 947
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