An instantaneous displacement of a simple harmonic oscillator is x=A (ω t+π / 4) . Its speed will be maximum at time

Correct answer: A. π / 4 ω Velocity, v=(d x)/(d t)=-A ω (ω t+π / 4) Velocity will be maximum, when ω t+π / 4=π / 2 or ω t=π / 2-π / 4=π / 4 or t=π / 4 ω

BITSAT 2020

Exam: BITSAT
Year: 2020
Subject: Physics
Chapter: Oscillations

BITSAT 2020 · Physics · Oscillations

An instantaneous displacement of a simple harmonic oscillator is...

An instantaneous displacement of a simple harmonic oscillator is

x=A \cos (\omega t+\pi / 4)

. Its speed will be maximum at time

Options

A $\pi / 4 \omega$
B $\pi / 2 \omega$
C $\pi / \omega$
D $2 \pi \omega$

Correct answer

A. $\pi / 4 \omega$

Step-by-step solution

Velocity,

v=\frac{d x}{d t}=-A \omega \sin (\omega t+\pi / 4)

Velocity will be maximum, when

\omega t+\pi / 4=\pi / 2

\omega t=\pi / 2-\pi / 4=\pi / 4

t=\pi / 4 \omega

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