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Periodic Motion and the SHM Equation for JEE: 14 solved questions

Real JEE paper questions on periodic motion and the shm equation, part of oscillations. Each opens with the options, the correct answer and a step-by-step solution. Papers run from 2005 to 2026. No sign-in needed to read them.

What this topic asks

• Displacement equation and phase — 7 questions
• Force law, potential energy and circular projection — 4 questions
• Identifying SHM — 3 questions

All 14 questions with solutions

• Match List-I with List-II. List-I: (A) sin²(ω t) (B) sin³(2ω t) (C) sin(ω t)+cos(πω t) (D) cos ω t+cos 2ω t L… JEE Main 5th April 2nd Shift 2026
• The kinetic energy of a simple harmonic oscillator is oscillating with angular frequency of 176 rad s⁻¹. The… JEE Main 21st Jan 2nd Shift 2026
• Given below are two statements. One is labelled as Assertion (A) and the other is labelled as Reason (R). Ass… JEE Main 28th Jan 2nd Shift 2025
• For particle P revolving round the centre O with radius of circular path r and angular velocity ω, as shown i… JEE Main 8th April 2nd Shift 2023
• A particle executes S.H.M. of amplitude A along the x-axis. At t=0 the position of the particle is x=A/2 and… JEE Main 10th April 1st Shift 2023
• The motion of a mass on a spring of spring constant K is as shown in the figure. The equation of motion is x(… JEE Main 22nd July 2nd Shift 2021
• The function of time representing a simple harmonic motion with a period of π/ω is JEE Main 18th March 2nd Shift 2021
• The point A moves with a uniform speed along the circumference of a circle of radius 0.36 m and covers 30° in… JEE Main 25th Feb 2nd Shift 2021
• Y=A sin(ω t+φ₀) is the time-displacement equation of a SHM. At t=0 the displacement of the particle is Y=A/2… JEE Main 25th Feb 2nd Shift 2021
• A particle executes simple harmonic motion and is located at x=a, b and c at times t₀, 2t₀ and 3t₀ respective… JEE Main Online 2018
• If a simple harmonic motion is represented by (d²x)/(dt²)+α x=0, its time period is JEE Main 2005
• The function sin²(ω t) represents JEE Main 2005
• The potential energy of a particle of mass 4 kg in motion along the x-axis is given by U=4(1-cos 4x) J. The t… JEE Main 28th July 2nd Shift 2022
• A particle executes simple harmonic motion represented by the displacement function x(t)=A sin(ω t+φ). If the… JEE Main 27th July 2nd Shift 2021