Question Detail

PHY 104 Oscillatory Motion Objective Question

Question

What is the correct mathematical expression for the amplitude A(t) of a damped oscillation at any given time t?
Options
A A(t) = A₀e^(-γt/2)
B A(t) = A₀e^(-t/2τ)
Correct Answer
C A(t) = A₀e^(-γt)
D A(t) = A₀sin(ωt + δ)e^(-γt/2)
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'.

Question Info