Schooling · Class 11 · Physics · Oscillations · Chapter on a page
CBSE Class 11 · Physics · NCERT Physics Part-II
Oscillations: chapter on a page
A cut of Shishya's notes for this chapter: the first paragraph of the introduction and the key ideas, formulas and facts, common mistakes and quick revision lists, word for word. Nothing is added or reworded; the worked examples are left out (they are on the chapter page).
About the notes: Written by Shishya's AI on 27 Sept 2026 from the chapter's title and class level, in Shishya's own words — not a copy or summary of the textbook. Read the official chapter for the book's own text, activities and exercises.
Fact-checked on 21 Oct 2026: an AI-assisted check of this note against cited sources; the errors it found were corrected that day. Some errors may remain.
Mind map
Drawn from the same notes by a fixed rule (no AI): each label is the item's own words — its bold term, its label before a colon, a short formula as written, or its first words.
The mind map as a list
- Key ideas
- Periodic motion
- Oscillatory (vibratory) motion
- Simple harmonic motion (SHM)
- In SHM the displacement varies…
- Velocity in SHM is v = −Aω sin(ωt +…
- Acceleration in SHM is a = −ω²x; it…
- Total mechanical energy E = (1/2)kA²…
- Formulas and facts
- T = 1/f
- ω = 2πf = 2π/T
- x = A cos(ωt + φ)
- v = dx/dt = −Aω sin(ωt + φ)
- a = dv/dt = −ω²x
- T (spring) = 2π√(m/k)
- T (pendulum) = 2π√(L/g)
- Worked examples
- Spring–mass system
- Simple pendulum on Earth
- Energy at a given displacement
- Watch out for
- Assuming acceleration is maximum at…
- Confusing frequency f (in Hz) with…
- Using T = 2π√(L/g) for large swing…
- Forgetting the negative sign in F =…
- Treating amplitude and displacement…
What this chapter is about
Oscillations describe any motion that repeats itself in a regular pattern about a central, equilibrium position. A child on a swing, the bob of a pendulum, the vibrating string of a sitar, and the back-and-forth motion of atoms in a solid are all examples. This chapter introduces the physics behind such periodic motion, focusing on the simplest and most important case: simple harmonic motion (SHM).
Key ideas
- Periodic motion is any motion that repeats exactly after a fixed time interval called the time period T. The reciprocal 1/T is the frequency f (unit: hertz, Hz).
- Oscillatory (vibratory) motion is periodic motion where the object moves to and fro about a mean position; not every periodic motion is oscillatory (e.g. uniform circular motion is periodic but not oscillatory).
- Simple harmonic motion (SHM) is oscillatory motion in which the restoring force F is directly proportional to the displacement x from equilibrium and directed opposite to it: F = −kx, where k is a positive constant.
- In SHM the displacement varies sinusoidally with time: x(t) = A cos(ωt + φ), where A is the amplitude, ω = 2πf is the angular frequency (rad/s), and φ is the initial phase.
- Velocity in SHM is v = −Aω sin(ωt + φ); it is maximum at the mean position and zero at the extreme positions.
- Acceleration in SHM is a = −ω²x; it is maximum at the extremes (magnitude Aω²) and zero at the mean position.
- Total mechanical energy E = (1/2)kA² remains constant during SHM; kinetic and potential energies interchange but their sum does not change (in the absence of damping).
- For a mass m on a spring of constant k, the time period T = 2π√(m/k). For a simple pendulum of length L (small-angle oscillations), T = 2π√(L/g), where g is acceleration due to gravity.
Formulas and facts to remember
- Expression: T = 1/f · Meaning: Time period (s) equals reciprocal of frequency (Hz).
- Expression: ω = 2πf = 2π/T · Meaning: Angular frequency in rad/s.
- Expression: x = A cos(ωt + φ) · Meaning: Displacement in SHM; A is amplitude, φ is phase constant.
- Expression: v = dx/dt = −Aω sin(ωt + φ) · Meaning: Velocity in SHM; maximum value v_max = Aω.
- Expression: a = dv/dt = −ω²x · Meaning: Acceleration in SHM; always opposite to displacement.
- Expression: T (spring) = 2π√(m/k) · Meaning: Time period of a mass–spring oscillator.
- Expression: T (pendulum) = 2π√(L/g) · Meaning: Time period of a simple pendulum (small angle).
- Expression: E = (1/2)kA² = (1/2)mω²A² · Meaning: Total mechanical energy in SHM (constant).
- Expression: KE = (1/2)mv² ; PE = (1/2)kx² · Meaning: Kinetic and potential energies; their sum equals E.
Common mistakes
- Assuming acceleration is maximum at the mean position → In SHM acceleration is zero at the mean position; it is maximum at the extremes where restoring force is greatest.
- Confusing frequency f (in Hz) with angular frequency ω (in rad/s) → Always check units; ω = 2πf.
- Using T = 2π√(L/g) for large swing angles → This formula holds only for small angles (typically less than about 15°). For larger angles, the motion is still periodic but not exactly SHM.
- Forgetting the negative sign in F = −kx or a = −ω²x → The minus sign shows the force or acceleration opposes the displacement; it is essential for SHM.
- Treating amplitude and displacement as the same quantity → Amplitude A is the maximum displacement; x changes with time while A stays constant.
Quick revision
- SHM occurs when the restoring force is proportional to displacement and opposite in direction: F = −kx.
- Displacement x = A cos(ωt + φ); velocity and acceleration follow by differentiation.
- Time period for a spring: T = 2π√(m/k); for a simple pendulum: T = 2π√(L/g).
- Total mechanical energy (1/2)kA² stays constant; KE and PE exchange during each cycle.
- At the mean position: velocity is maximum, acceleration is zero. At extreme positions: velocity is zero, acceleration is maximum.