It takes 20.0 s for a exponentially damped harmonic oscillator to have its amplitude decrease from its initial value to one-half the initial value. How long does it take the amplitude to decrease from its initial value to one-fourth the initial value?
A)40.0 s
B)60.0 s
C)50.0 s
D)80.0 s
E)30.0 s

Question

Quizplus · Accepted Answer

The amplitude of an exponentially damped harmonic oscillator decreases according to the formula A(t) = A_0 * e^(-bt), where A_0 is the initial amplitude and b is the damping constant. If it takes 20.0 s for the amplitude to decrease to half, it will take another 20.0 s to decrease to one-fourth, because the amplitude decreases by half every 20.0 s. Therefore, it takes a total of 40.0 s to decrease to one-fourth the initial value.

It Takes 20