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Exam level3 past questions

Basics of Simple Harmonic Motion (SHM)

Understand the defining features of SHM, including its standard equations, conditions, and the relationship between displacement, velocity, and acceleration.

Why this shows up in the exam

NEET often tests your ability to recognize and analyze SHM from equations and motion descriptions.

How NEET tests this

Direct recall · 2 QsStatement analysisNumerical

Learn the idea

Simple Harmonic Motion is the motion where the restoring acceleration is directly proportional to the displacement from the equilibrium position and always opposite in direction. The single insight is to check the sign: a must equal –(constant)×(displacement).

🧠 Memory hook: SHM = ‘S’ame ‘H’ooke’s ‘M’otion: a = –k·(x‑equilibrium) – the acceleration always pulls back.

Get this one clearly and it pays off every single time it shows up in the paper. 🎯

Formulas & facts to keep ready

  • a = –ω²x (acceleration opposite to displacement)
  • Equation of motion: d²x/dt² + ω²x = 0
  • ω = 2π/T = √(k/m) for a mass‑spring system
  • Maximum speed occurs at equilibrium, zero speed at extreme positions
  • If the origin is shifted, displacement must be measured from the new equilibrium (x‑x₀)
  • Energy remains constant: ½kA² = ½mv² + ½kx²

How to approach it

  1. 1Identify the acceleration expression in the given equation
  2. 2Check whether it can be written as –(constant)×(displacement from some equilibrium point)
  3. 3If a constant term appears, rewrite displacement as (x – x₀) to locate the true equilibrium
  4. 4Confirm the form d²x/dt² + ω²x = 0; then the motion is SHM
  5. 5Use ω to find period T = 2π/ω if required

Worked example — watch it click

Which one of the following equation of motion represents simple harmonic motion? (a) Acceleration = - k(x+a) (b) Acceleration = k(x+a) (c) Acceleration = kx (d) Acceleration = - k₀x+k₁x₂ where k, k₀, k₁ and a are all positive.

  • ✅Acceleration = - k(x+a)
  • B)Acceleration = k(x+a)
  • C)Acceleration = kx
  • D)Acceleration = - k₀x+k₁x₂

The concept behind this problem

The example asks you to recognise that the defining condition for SHM is a = –k·(displacement from equilibrium); option (a) satisfies this after redefining the origin at x = –a.

Step by step

  1. 1SHM requires acceleration ∝ -(displacement from equilibrium).
  2. 2If we define X = x + a as displacement from a new origin at x = -a, then a = -kX represents SHM about that point.
  3. 3Option (a) can be rewritten as a = -k(displacement from x = -a), which is SHM.

Watch out

A common mistake is to pick option (c) kx, forgetting that SHM requires a negative sign before the displacement term.

Common slip-ups that cost marks

  • •Missing the negative sign – a positive proportionality (kx) is NOT SHM
  • •Treating a constant offset as part of the restoring force without shifting the origin
  • •Confusing angular frequency ω with linear frequency f; period is 2π/ω, not 1/ω

🌟 That's the whole idea — you've got this. Try the practice set below; every question you attempt makes it stick a little harder.

Practise it

These are real questions from past NEET papers that test this exact idea.

Question 1 of 3NEET 1992

A simple harmonic oscillator has an amplitude A and time period T. The time required by it to travel from x = A to x = A/2 is:

Push further

More challenging

2 harder questions built from the past papers above — a step up in difficulty, with distractors designed so you can't get there by elimination. Written and checked by our reviewers, not from a real paper.

Question 1 of 2

A particle moves such that its potential energy U(x) = (1/2)kx² - bx + c, where k, b, and c are positive constants. Which of the following statements about its motion is correct?

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