A body is in simple harmonic motion with time period T = 0.5s and amplitude A = 1cm . Find the average velocity in the interval in which it moves from equilibrium position to half of its amplitude.

Correct answer: D. 12cm/s ∴ x = Asin (A)/(2) = Asin = (π)/(6) t = (π)/(6ω) = (π)/(6 × 2 π) t = (T)/(12) ∴ Timetakentoreachfromx = 0tox = (A)/(2)is(T)/(12) ∴ Averagevelocity = (Displacement)/(Time) = (A / 2)/(T / 12) = (A)/(T) × 6 = (6 × 1)/(0.5) = 12cm / s

JEE Main 201419 AprilOnline

Exam: JEE Main
Year: 2014
Date: 19 April
Mode: Online
Subject: Physics
Chapter: Oscillations

JEE Main 2014 · 19 April · Online · Physics · Oscillations

A body is in simple harmonic motion with time period T = 0.5s and...

A body is in simple harmonic motion with time period

T = 0.5\text{s}

and amplitude

A = 1\text{cm}

. Find the average velocity in the interval in which it moves from equilibrium position to half of its amplitude.

Options

A $16\text{cm/s}$
B $6\text{cm/s}$
C $4\text{cm/s}$
D $12\text{cm/s}$

Correct answer

D. $12\text{cm/s}$

Step-by-step solution

∴ x = Asin \omegat

\dfrac{A}{2} = Asin \omegat

\omegat = \dfrac{\pi}{6}

t = \dfrac{\pi}{6\omega}

= \dfrac{\pi}{6 \times 2 \pi}

t = \dfrac{T}{12}

∴ Timetakentoreachfromx = 0tox = \dfrac{A}{2}is\dfrac{T}{12}

∴ Averagevelocity = \dfrac{Displacement}{Time}

= \dfrac{A / 2}{T / 12}

= \dfrac{A}{T} \times 6

= \dfrac{6 \times 1}{0.5}

= 12cm / s

Practice Oscillations on Quantrex Academy →

More from Oscillations

A tank contains two immiscible liquids of densities 6ρ and 2ρ . The higher density liquid… JEE Advanced 2026 The frequency of oscillation of a mass m suspended by a spring is v_1 . If the length of… JEE Main 2026 A spring stretches by 2 mm when it is loaded with a mass of 200 g. From equilibrium… JEE Main 2026 A particle is executing simple harmonic motion. Its amplitude is A and time period is 5… JEE Main 2026 Match List-I with List-II. List-I List-II A. ^2 ω t I. Periodic with time period T =… JEE Main 2026 A uniform disc of radius R and mass M is free to oscillate about the axis A as shown in… JEE Main 2026 The velocity of a particle executing simple harmonic motion along x -axis is described as… JEE Main 2026 The equation of motion of a particle is given by x = a (50t + (π)/(3)) cm. The particle… JEE Main 2026 Full Oscillations list All JEE Main PYQs