Question

The amplitude of an oscillator decreases to$36.8\%$of its initial value in$10.0\mathrm{s}$What is the value of the time constant?

Short answer

Time constant has the value of$\tau =5\mathrm{s}$.

Step-by-step solution

Introduction.

Oscillation is the repeated or recurrent oscillation of a statistic around a central value or between two or more states, usually in time.

A physiological motion is clearly perceived by the term vibration. Oscillation can be seen in a pendulum bob and flow of electrons.

Explanation

A decelerated oscillator's output diminishes continuously with increasing:

$A=A_0{e}^{-\frac{t}{2\tau }}$

The time constant $T$ is used here. When you use $\frac{A}{A_0}=0.368$ and the logarithmic function, you get

$\tau =-\frac{t}{2\ln \left(0.368\right)}=5\mathrm{s}$