Question

Given a typical value of the decay constant, tau, to be 16s, How long should you wait before the amplitude of the damped oscillations is 1% of the original amplitude?

Answer 1

The hint provided in this question is the envelope that defines the amplitude of the damped oscillations as a function of time.

As a result the related formula is

A _damped = A_original

Given;

A _damped = 1% x A_original

=0.01 A_original

So, 0.01 A_original =   A_original

_So, =0.01

So, t=0.2878 s

So, one should wait 0.2878 s before the amplitude of the damped oscillations is 1% of the original amplitude.

Answer : 0.288 s

HOPE THE ABOVE ANSWER CLARIFIES THE DOUBT. ALL THE BEST TO THE STUDENT IN HIS COURSE WORK.