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JEE Main & Advanced / Physics / Chapter 14

Simple Harmonic Motion

Learn SHM as a complete language of restoring-force motion: equations, energy, phase, springs, and oscillation timing.

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JEE Intro

How to Think About Simple Harmonic Motion

Learn SHM as a complete language of restoring-force motion: equations, energy, phase, springs, and oscillation timing.

This chapter is written as original Learn at My Place teaching copy. The aim is to give you the JEE decision-making layer: what equation to trust, what approximation is valid, and where exam traps usually appear.

Read the full note once, then revisit the quick revision block before solving your own practice questions.

Problem Method

How to Solve Simple Harmonic Motion Questions

1. Model the Situation

Draw the body, path, field, graph, or interaction first. Label known quantities and choose sign convention before writing equations.

2. Pick the Governing Law

Decide whether the problem is about conservation, force balance, energy, momentum, fields, or graph interpretation.

3. Check the Edge Case

Verify units, limiting values, direction, and whether approximation assumptions are valid for JEE Main and Advanced options.

Section A

Notes: Simple Harmonic Motion

Original teaching copy for Learn at My Place
1. SHM Equations and Kinematics2. Energy and Spring Systems

1. SHM Equations and Kinematics

A particle executes SHM when acceleration is proportional to displacement and directed toward the mean position:

a=−ω2xa = -\omega^2x
A common form is:
x=Asin⁡(ωt+ϕ)orAcos⁡(ωt+ϕ)x = A\sin(\omega t + \phi) \quad \text{or} \quad A\cos(\omega t + \phi)

Useful relations:

v=±ωA2−x2,vmax=Aωv = \pm \omega\sqrt{A^2 - x^2}, \qquad v_{max} = A\omega

2. Energy and Spring Systems

Total energy in SHM remains constant:

E=12kA2=12mω2A2E = \frac12 kA^2 = \frac12 m\omega^2A^2
Kinetic energy is maximum at mean position and potential energy is maximum at extremes.

For a mass-spring system:

T=2πmkT = 2\pi\sqrt{\frac{m}{k}}
Equivalent spring constant ideas are heavily used in JEE spring-combination questions.

Quick Revision

Last 5-Minute Recall

JEE exam rule: First identify the governing principle. Most errors happen because students choose the wrong framework before they start the algebra.
Restoring-force definition of SHM
Displacement, velocity, acceleration relations
Energy distribution during oscillation
Spring-mass systems and time period
Finished this topic?

Keep the practice loop moving

Move straight from chapter-wise questions into a subject test, then loop back into weaker areas instead of ending the session here.

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