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Oscillations

NCERT Class 11 Physics Chapter 13

Oscillations for Class 11 Physics, JEE and NEET: periodic motion, simple harmonic motion, energy in SHM, spring oscillations and the simple pendulum.

8 topics Updated 8 Nov 2026

For: Class 11, JEE and NEET, unless a topic says otherwise

In the syllabus: JEE Class 11 syllabus, NEET Class 11 syllabus

With your textbook

NCERT Physics Part II (Class 11), Chapter 13 “Oscillations”, reprint 2026-27.

Open the official NCERT chapter (PDF, 1.6 MB, ncert.nic.in)

Checked on 19 Oct 2026.

Learn in this order

  1. Periodic and oscillatory motion

    The difference, examples, period and frequency, displacement and periodic functions.

    NCERT Section 13.2 14 min read 5 solved examples 6 practice questions

  2. Simple harmonic motion

    The definition, x(t) = A cos(ωt + φ), amplitude, phase, phase constant and angular frequency.

    NCERT Section 13.3 15 min read 5 solved examples 6 practice questions

  3. SHM and uniform circular motion

    The reference circle, x and y projections, clockwise motion, solved examples.

    NCERT Section 13.4 13 min read 5 solved examples 6 practice questions

  4. Velocity and acceleration in SHM

    v = −ωA sin(ωt + φ), a = −ωx, speed at any position, phase relations, solved examples.

    NCERT Section 13.5 11 min read 5 solved examples 6 practice questions

  5. Force law for SHM

    Restoring force F = −kx, force constant k = mω, spring period T = 2π√(m/k), spring combinations.

    NCERT Section 13.6 13 min read 5 solved examples 6 practice questions

  6. Energy in SHM

    Kinetic and potential energy, constant total energy E = ½kA, energy graphs and solved examples.

    NCERT Section 13.7 11 min read 5 solved examples 6 practice questions

  7. The simple pendulum

    Forces on the bob, deriving T = 2π√(L/g), the small-angle limit, seconds pendulum and solved examples.

    NCERT Section 13.8 13 min read 5 solved examples 6 practice questions

  8. Experiment: simple pendulum and loss of energy

    Timing the period, finding g, and plotting the square of the amplitude against time to show energy loss.

    JEE and NEET only 14 min read 5 solved examples 6 practice questions

Key formulas in this chapter

Periodic and oscillatory motion

  • ν = 1/T; 1 Hz = 1 s
  • T = 2π/ω for A cos ωt or A sin ωt
  • A sin ωt + B cos ωt = D sin(ωt + φ)
  • D = √(A + B), tan φ = B/A

Simple harmonic motion

  • x(t) = A cos(ωt + φ)
  • ω = 2π/T = 2πν
  • phase = ωt + φ; phase constant = φ
  • x(0) = A cos φ

SHM and uniform circular motion

  • x(t) = A cos(ωt + φ) (x-projection, anticlockwise)
  • y(t) = A sin(ωt + φ) (y-projection, π/2 behind)
  • x(t) = A cos(ωt − φ) (clockwise from angle φ)
  • ω = 2π/T (angular speed of the reference particle)

Velocity and acceleration in SHM

  • v(t) = −ωA sin(ωt + φ)
  • a(t) = −ωx = −ωA cos(ωt + φ)
  • v = ±ω√(A − x)
  • vmax = ωA (at x = 0); amax = ω2A (at x = ±A)

Force law for SHM

  • F = −kx
  • k = mω; ω = √(k/m)
  • T = 2π√(m/k)
  • Parallel: k = k + k; series: k = kk/(k + k)

Energy in SHM

  • K = ½kA sin(ωt + φ) = ½k(A − x)
  • U = ½kx = ½kA cos(ωt + φ)
  • E = ½kA = ½mωA (E = K + U)
  • K = U at x = ±A/√2

The simple pendulum

  • τ = −mgL sin θ
  • α = −(mgL/I)θ (small θ, in radians)
  • T = 2π√(I/mgL)
  • T = 2π√(L/g)
  • L = gT/4π; g = 4πL/T

Experiment: simple pendulum and loss of energy

  • T = 2π√(L/g); g = 4πL/T
  • T = t/n (n oscillations in time t)
  • E = mgA/(2L) (small swings)
  • Δg/g ≈ ΔL/L + 2ΔT/T (first-order worst-case uncertainty)

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