In damped harmonic oscillation, the amplitude of oscillation becomes one third after 2 second. If A0 is initial amplitude of oscillation, th

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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

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Sigridomena 3 months 2021-08-15T07:41:04+00:00 1 Answers 6 views 0

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    2021-08-15T07:42:32+00:00

    Answer:

    A=\frac{A_0}{\sqrt 3}

    Explanation:

    Initial amplitude=A_0

    We are given that

    Amplitude after 2 s=A=\frac{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

    \frac{A_0}{3}=A_0e^{-2\alpha}

    \frac{1}{3}=e^{-2\alpha}

    3=e^{2\alpha}

    ln 3=2\alpha

    \alpha =\frac{ln 3}{2}=ln\sqrt 3

    e^{\alpha}=\sqrt 3}

    When t=1 s

    A=A_0e^{-\alpha}=\frac{A_0}{\sqrt 3}

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