Question

The amplitude of an oscillator decreases to 36.8% of its initial value in 10.0 s. What is the value of the time constant?

Short answer

The Time Constant is 5.0

Step-by-step solution

Introduction

The amplitude fordamped harmonic motion is as follows

$X=X_o{e}^{t/2\tau }$

where

t is the time.

$\tau$is the time constant.

X is the instantaneous value of amplitude.

$X_0$is the initial value ofamplitude.

Substituting the values

Substituting the values

$$\begin{gathered} 0.368=e^{-10/2\tau } \\ \ln (0.368)=\frac{-10}{2\tau } \\ \tau =\frac{-10}{-1.9994}=5.0 \end{gathered}$$