Amplitude of an underdamped oscillation (12-35)

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Question

The amplitude of an underdamped oscillator at time \(t\) after it is set in motion...
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Review

If \(b\) is relatively small (less than \(2\sqrt{km}\)), the system still oscillates but with ever-decreasing amplitude. (This is what you observed in the experiment we described at the beginning of this section about letting your arm swing.) This is called \(\textbf{underdamped oscillation}\). If the amplitude when the oscillation begins at \(t = 0\) is \(A\), the amplitude at a later time \(t\) is: