Oscillations Notes for NEET and JEE Main 2027: Key Points and PDF

Oscillations is Chapter 13 of NCERT Class 11 Physics (Part II) and the first half of Unit 10, Oscillations and Waves, in both the NEET UG and JEE Main syllabus. These notes cover periodic and oscillatory motion, simple harmonic motion, phase, velocity and acceleration, the spring force law, energy in SHM and the simple pendulum, with a free PDF.

Oscillations Notes for NEET and JEE Main

Section-wise key points from NCERT Chapter 13, SHM formula tables, high-yield facts and common mistakes for 2027 revision.

Oscillations at a Glance

The topic list follows the NEET UG 2026 syllabus released by the National Medical Commission (NMC) on 22 December 2025 and the JEE Main 2026 syllabus published by the National Testing Agency (NTA). Both stay the reference until the 2027 syllabi are out. The full lists are on the NEET syllabus and JEE Main syllabus pages.

Periodic and Oscillatory Motion

A motion that repeats itself at regular intervals is periodic; a periodic to-and-fro motion about a mean position is oscillatory.

• Every oscillatory motion is periodic, but every periodic motion need not be oscillatory. Circular motion is periodic but not oscillatory.
• At the equilibrium position the net external force is zero; when the body is displaced, a force tries to bring it back, giving oscillations.
• Oscillation and vibration differ only in frequency: low-frequency motion is usually called oscillation, high-frequency motion vibration.
• Period T is the least time after which the motion repeats. Frequency ν = 1/T, measured in hertz (1 Hz = 1 s⁻¹).
• NCERT example: a heart beating 75 times a minute has ν = 1.25 Hz and T = 0.8 s.
• ‘Displacement’ can be any changing physical quantity, such as the angle of a pendulum or the voltage in an AC circuit.
• f(t) = A cos ωt is periodic with T = 2π/ω. Fourier: any periodic function can be written as a superposition of sine and cosine functions of different periods.

Simple Harmonic Motion: Equation and Phase

In SHM the displacement from the equilibrium position varies as a sine or cosine function of time: x(t) = A cos(ωt + φ).

• The forms A cos ωt + B sin ωt, A cos(ωt + α) and B sin(ωt + β) are equivalent descriptions of SHM.
• The period of SHM does not depend on amplitude, energy or phase constant.
• For a given ω, two initial conditions (for example initial position and velocity) fully determine the motion.

SHM and Uniform Circular Motion

If a particle moves uniformly on a circle, the projection of its position on any diameter executes SHM.

• The moving particle and its circle are called the reference particle and the reference circle.
• Projection on the x-axis gives x = A cos(ωt + φ); projection on the y-axis gives y = A sin(ωt + φ), the same SHM shifted in phase by π/2.
• The radius of the circle equals the amplitude, and the angular speed of the reference particle equals ω.

Velocity and Acceleration in SHM

Velocity and acceleration in SHM are periodic with the same period T as displacement but differ in phase.

• v(t) = −ωA sin(ωt + φ); velocity amplitude v_m = ωA.
• a(t) = −ω²A cos(ωt + φ) = −ω²x(t); acceleration amplitude a_m = ω²A.
• Acceleration is proportional to displacement and always directed towards the mean position.

Force Law for SHM: Oscillations of a Spring

A motion is simple harmonic only when the restoring force is proportional to displacement and opposite to it: F = −kx.

• From Newton’s second law, F = ma = −mω²x, so k = mω² and ω = √(k/m).
• Period of a block of mass m on a spring of force constant k: T = 2π√(m/k). Such a system is a linear oscillator.
• Force constant (spring constant) k has the SI unit N m⁻¹.
• NCERT example: a mass between two identical springs of constant k on either side oscillates with T = 2π√(m/2k).
• Not every periodic motion is SHM; only motion governed by F = −kx is.

Energy in Simple Harmonic Motion

Kinetic and potential energy keep changing during SHM, but their sum stays constant when there is no friction.

• Both K and U are always positive in SHM.
• Total energy is proportional to the square of the amplitude.

The Simple Pendulum

A bob of mass m on a string of length L swinging through small angles performs approximately simple harmonic motion.

• The radial force (T − mg cos θ) provides the centripetal force but no torque about the support; the tangential component mg sin θ provides the restoring torque τ = −mgL sin θ.
• For small θ (in radians), sin θ ≈ θ, so the angular acceleration is proportional to −θ and the motion is SHM.
• Time period: T = 2π√(L/g).
• For small angles, the period does not depend on the mass of the bob or the amplitude.
• Galileo is said to have measured the periods of a swinging chandelier using his pulse beats.

Most-asked Facts for NEET and JEE Main: Oscillations

Revise these one-line facts from the NCERT chapter just before the exam.

• ν = 1/T; ω = 2π/T = 2πν.
• x = A cos(ωt + φ); v = −ωA sin(ωt + φ); a = −ω²x.
• Maximum speed ωA at the mean position; maximum acceleration ω²A at the extremes.
• SHM force law: F = −kx with k = mω².
• Spring–mass system: T = 2π√(m/k).
• Simple pendulum (small angles): T = 2π√(L/g).
• Total energy in SHM = ½kA², constant in time.
• K and U each vary with period T/2.
• Period of SHM is independent of amplitude.
• SHM is the projection of uniform circular motion on a diameter.
• Every oscillatory motion is periodic, not vice versa.

Common Mistakes to Avoid

Watch for these mix-ups when you answer questions on this chapter.

• Calling every periodic motion SHM. Uniform circular motion and planetary motion are periodic but not simple harmonic.
• Placing maximum acceleration at the mean position. Acceleration is zero there and maximum at the extremes.
• Taking the period of kinetic or potential energy as T. Each varies with period T/2.
• Using T = 2π√(L/g) for large angles. It holds only when sin θ ≈ θ.
• Thinking a heavier bob changes the period of a simple pendulum. For small angles T depends only on L and g.
• Using degrees instead of radians for θ in sin θ ≈ θ or in the phase ωt + φ.
• Writing a = −ωx instead of a = −ω²x.

Oscillations Notes PDF and Related Pages

Download the AglaSem Class 11 Physics notes for Oscillations and Waves (key notes and important questions with answers) free: View PDF. The same PDF covers Waves. It also has older topics, such as damped and forced oscillations, that are not in the rationalised NCERT chapter.

• All chapters: Physics notes for NEET and JEE Main
• Full topic list: NEET syllabus and JEE Main syllabus
• Practice: NEET question papers and JEE Main question papers
• Source text: NCERT Chapter 13 (NCERT, Class 11 Physics Part II)

Physics Notes for NEET and JEE Main: All Chapters

• Units and Measurement
• Motion in a Straight Line
• Motion in a Plane
• Laws of Motion
• Work, Energy and Power
• Systems of Particles and Rotational Motion
• Gravitation
• Mechanical Properties of Solids
• Mechanical Properties of Fluids
• Thermodynamics
• Kinetic Theory of Gases
• Oscillations
• Waves
• Thermal Properties of Matter
• Electric Charges and Fields
• Electrostatic Potential and Capacitance
• Current Electricity
• Moving Charges and Magnetism
• Magnetism and Matter
• Electromagnetic Induction
• Electromagnetic Waves
• Ray Optics and Optical Instruments
• Wave Optics
• Dual Nature of Radiation and Matter
• Atoms
• Nuclei
• Semiconductor Electronics

All chapters with key points and notes PDFs are on the Physics notes for NEET and JEE Main page.

Oscillations Notes for NEET and JEE Main FAQs