Question Detail
Question
What is the correct mathematical expression for the amplitude A(t) of a damped oscillation at any given time t?
Correct Answer
Option B is the correct answer.
Detailed Explanation
The text on page 22, under 'Damping Parameter and Time Constant', states: 'The amplitude of the damped oscillation at any given time is given by A(t) = A₀e^(-γt/2) = A₀e^(-t/2τ)'. Option A is also correct but option B uses τ, the time constant, which is a common way to express it. Option B is more direct with the definition of τ. Option D includes the sinusoidal part which describes the position, not just the amplitude.
Hint
Look for the formula relating amplitude to the time constant τ, as presented on page 22 under 'Damping Parameter and Time Constant'.