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Simple Harmonic Motion — Revision Notes

NIOS · Class 12 · Physics

Simple Harmonic Motion revision notes for NIOS Class 12 Physics: 4 topics in quick points. Part of the NIOS Class 12 Physics syllabus.

45 questions37 flashcards19 formulas & key relations5 concepts

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A comparison chart distinguishing between periodic motion and oscillatory motion, providing clear definitions and examples for each category. Examples for periodic motion could include Earth's rotatio
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Key Topics to Revise

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1. Periodic Motion and Oscillatory Motion

  • A motion that repeats itself after a fixed interval of time is called Periodic Motion. Example: revolution of Earth around the Sun, motion of clock hands.
  • Oscillatory Motion is a to-and-fro motion about a fixed mean (equilibrium) position. Example: swinging pendulum, vibrating tuning fork.
  • Key Rule: Every oscillatory motion is periodic, but every periodic motion is NOT necessarily oscillatory.
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2. Simple Harmonic Motion – Definition, Equation and Circle of Reference

  • SHM is defined as the oscillatory motion in which the restoring force acting on the particle is directly proportional to its displacement from the mean position and is always directed towards the mean
  • Mathematically: F = –kx, where k is the force constant (also called spring constant). The negative sign shows the force is always opposite to displacement.
  • SHM can be understood as the projection of uniform circular motion on the diameter of the circle. This is called the 'Circle of Reference' or 'Reference Circle' concept.
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3. Time Period of Common SHM Systems

  • The time period formula T = 2π√(m/k) applies to all spring-mass systems (horizontal and vertical).
  • For a simple pendulum: T = 2π√(l/g). Note that the time period depends only on length l and acceleration due to gravity g — NOT on mass of the bob or amplitude (for small oscillations).
  • For vertical oscillations of a spring-mass system: T = 2π√(m/k). Gravity does NOT affect the time period of vertical spring oscillations because the equilibrium position shifts but the restoring force
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4. Energy in Simple Harmonic Motion

  • The total mechanical energy of a simple harmonic oscillator is constant (conserved) and equals E = ½mω²a² = ½ka².
  • Kinetic Energy (K) at displacement y: K = ½mω²(a² – y²). Maximum at y = 0 (mean position) and zero at y = ±a (extreme positions).
  • Potential Energy (U) at displacement y: U = ½mω²y² = ½ky². Minimum (zero) at mean position and maximum at extreme positions.

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Key Concepts

A motion that repeats itself afterA particle executes SHM if itSHM can be elegantly visualized as1HORIZONTAL

Frequently Asked Questions

What are the important topics in Simple Harmonic Motion for NIOS Class 12 Physics?
Key topics in Simple Harmonic Motion include Periodic Motion and Oscillatory Motion, Simple Harmonic Motion – Definition, Equation and Circle of Reference, Time Period of Common SHM Systems, Energy in Simple Harmonic Motion. Study these first, then practise questions on each for the NIOS Class 12 board exam.
How should I revise Simple Harmonic Motion for the NIOS Class 12 board exam?
Learn the core ideas first, then work through the 45 practice questions on Simple Harmonic Motion. Revise definitions regularly and use flashcards for quick recall before the exam.

Sources & Official References

Content is aligned to the official syllabus. Refer to the board website for the latest curriculum.

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