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Velocity and Acceleration in SHM for JEE: 31 solved questions

Real JEE paper questions on velocity and acceleration in shm, part of oscillations. Each opens with the options, the correct answer and a step-by-step solution. Papers run from 2006 to 2026. No sign-in needed to read them.

What this topic asks

• v-x and a-x relations — 20 questions
• Time, distance and displacement — 11 questions

All 31 questions with solutions

• A particle is executing simple harmonic motion. Its amplitude is A and time period T is 5 s. The time require… JEE Main 6th April 1st Shift 2026
• A particle is executing simple harmonic motion with time period 2 s and amplitude 1 cm. If D and d are the to… JEE Main 24th Jan 1st Shift 2025
• In a linear simple harmonic motion (SHM): (A) Restoring force is directly proportional to the displacement. (… JEE Main 15th April 1st Shift 2023
• A particle executes simple harmonic motion between x=-A and x=+A. If the time taken by the particle to go fro… JEE Main 25th Jan 2nd Shift 2023
• When a particle executes simple harmonic motion, the nature of the graph of velocity as a function of displac… JEE Main 26th July 1st Shift 2022; 24th Feb 2nd Shift 2021; 26th Feb 2nd Shift 2021
• The displacement of a simple harmonic oscillator after 3 s, starting from its mean position, is equal to half… JEE Main 27th June 1st Shift 2022
• The equation of a particle executing simple harmonic motion is given by x=sin π(t+1/3) m. At t=1 s the speed… JEE Main 27th June 2nd Shift 2022
• A particle is making simple harmonic motion along the X-axis. If at distances x₁ and x₂ from the mean positio… JEE Main 20th July 2nd Shift 2021
• The displacement-time graph of a particle executing S.H.M. is given in the figure (the sketch is schematic an… JEE Main 2nd Sept 2nd Shift 2020
• A particle executes simple harmonic motion with an amplitude of 5 cm. When the particle is at 4 cm from the m… JEE Main 10th Jan 1st Shift 2019
• The ratio of maximum acceleration to maximum velocity in a simple harmonic motion is 10 s⁻¹. At t=0 the displ… JEE Main Online 2017
• A particle performs simple harmonic motion with amplitude A. Its speed is tripled at the instant that it is a… JEE Main 2016
• Two particles are performing simple harmonic motion in a straight line about the same equilibrium point. The… JEE Main 2016
• A particle moves with simple harmonic motion in a straight line. In the first τ s, after starting from rest,… JEE Main 2014
• If x, v and a denote the displacement, the velocity and the acceleration of a particle executing simple harmo… JEE Main 2009
• A point mass oscillates along the x-axis according to the law x=x₀ cos (ω t-π/4). If the acceleration of the… JEE Main 2007
• The displacement of an object attached to a spring and executing simple harmonic motion is given by x=2×10⁻²… JEE Main 2007
• The maximum velocity of a particle executing simple harmonic motion with an amplitude 7 mm is 4.4 m s⁻¹. The… JEE Main 2006
• The velocity of a particle executing simple harmonic motion along the x-axis is described by v²=50-x², where… JEE Main 4th April 1st Shift 2026
• The displacement of a particle executing SHM is given by x=10 sin (ω t+π/3) m. The time period of motion is 3… JEE Main 4th April 2nd Shift 2024
• A particle is doing simple harmonic motion of amplitude 0.06 m and time period 3.14 s. The maximum velocity o… JEE Main 6th April 1st Shift 2024
• The position, velocity and acceleration of a particle executing simple harmonic motion are found to have magn… JEE Main 9th April 1st Shift 2024
• A particle executes simple harmonic motion with an amplitude of 4 cm. At the mean position the velocity of th… JEE Main 27th Jan 1st Shift 2024
• A simple harmonic oscillator has an amplitude A and time period 6π s. Assuming the oscillation starts from it… JEE Main 29th Jan 2nd Shift 2024
• A particle performs simple harmonic motion with amplitude A. Its speed is increased to three times at an inst… JEE Main 31st Jan 1st Shift 2024
• The velocity of a particle executing SHM varies with displacement x as 4v²=50-x². The time period of oscillat… JEE Main 30th Jan 2nd Shift 2023
• A particle executes simple harmonic motion. Its amplitude is 8 cm and time period is 6 s. The time it will ta… JEE Main 27th June 2nd Shift 2022
• A body is performing simple harmonic motion with an amplitude of 10 cm. The velocity of the body was tripled… JEE Main 29th June 1st Shift 2022
• A particle performs simple harmonic motion with a period of 2 s. The time taken by the particle to cover a di… JEE Main 18th March 1st Shift 2021
• A particle executes S.H.M. with amplitude a and time period T. The displacement of the particle when its spee… JEE Main 26th Feb 2nd Shift 2021
• The time period of a simple pendulum is T. The time taken to complete 5/8 oscillations starting from the mean… JEE Main 26th Feb 2nd Shift 2021