Question

In damped harmonic oscillation, the amplitude of oscillation becomes one third after 2 second. If A0 is initial amplitude of oscillation, then amplitude after 1 second from start will be

Answer 1

`A=(A_0)/(\sqrt 3)`

Step-by-step explanation:

Initial amplitude=
`A_0`

We are given that

Amplitude after 2 s=A=
`(1)/(3)A_0`

We have to find the amplitude after 1 s.

We know that amplitude at any time t

`A=A_0e^(-\alpha t)`

Using the formula

`(A_0)/(3)=A_0e^(-2\alpha)`

`(1)/(3)=e^(-2\alpha)`

`3=e^(2\alpha)`

`ln 3=2\alpha`

`\alpha =(ln 3)/(2)=ln\sqrt 3`

`e^(\alpha)=\sqrt 3}`

When t=1 s

`A=A_0e^(-\alpha)=(A_0)/(\sqrt 3)`