The amplitude of an oscillator decreases to 692 of its init

The amplitude of an oscillator decreases to 69.2 % of its initial value in 26.5 s. What is the value of the time constant?

Solution

general equation :

A = A_max e^(-t/T)

given that : A = 0.692 A_max

inserting the values

0.692 A_max = A_max e^(-26.5/T)

0.692 = e^(-26.5/T)

- 0.368 = (-26.5/T)

T = 72.01 sec