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An instantaneous displacement of a simple harmonic oscillator is $\mathrm{x}=\mathrm{A} \cos (\omega \mathrm{t}+\pi / 4) .$ Its speed will be maximum at time
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$\pi / 4 \omega$
Velocity, $\mathrm{v}=\frac{\mathrm{dx}}{\mathrm{dt}}=-\mathrm{A} \omega \sin (\omega \mathrm{t}+\pi / 4)$
Velocity will be maximum, when $\omega t+\pi / 4=\pi / 2$ or $\omega t=\pi / 2-\pi / 4=\pi / 4$
or $t=\pi / 4 \omega$
Velocity will be maximum, when $\omega t+\pi / 4=\pi / 2$ or $\omega t=\pi / 2-\pi / 4=\pi / 4$
or $t=\pi / 4 \omega$
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