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CBSE Class 11 · Physics

Oscillations

Official NCERT chapter from Physics Part I–II (book code keph1). ExamMaster notes are original teaching at CBSE Class 11 depth.

This lesson follows the official chapter “Oscillations” in Physics Part I–II. The words below are ExamMaster’s teaching, not a paste from the book. Use the NCERT chapter for the classroom sequence; use these notes to hold the idea without copying exercises or figures.

  • CBSE Class 11
  • Medium level
  • 8 concepts

1Periodic and oscilatory motions

Periodic motion repeats after a period T; oscillatory motion is a to-and-fro about a mean. A swing is both; a uniform circle is periodic but not this to-and-fro on a line. The title’s “oscilatory” is this to-and-fro heading.

A one-way walk that never returns is not oscillatory.

Figure. Oscillatory motion is to-and-fro about a mean (the mass on the left returns through the same line). Periodic motion only has to repeat after a time T — a year of seasons repeats without the Earth travelling back and forth on a line. Every oscillatory motion is periodic; the converse is false.

How it works

  1. Name a repeat-time TPeriodic.
  2. Name a to-and-fro about a meanOscillatory.
  3. Keep a circle as periodic, not automatically SHM on a lineTwo words.

2Simple harmonic motion

Simple harmonic motion: acceleration toward the mean, size ∝ displacement — a = −ω² x as taught. A sine or cosine x(t) is the solution. SHM is this restore-rule, not every oscillation (a real bounce with extra friction is a cousin).

A to-and-fro with a constant restore-force (not ∝ x) is not SHM.

Figure. Simple harmonic motion is the special to-and-fro whose displacement from the mean is a cosine (or sine) of time. Here x = A\cos\omega t: the particle starts at the extreme +A when t=0, crosses the mean at T/4, and reaches -A at T/2. The mid-figure axis is x=0, not the bottom of the box.

How it works

  1. See F or a toward the mean and ∝ xThe test.
  2. Write a = −ω² xSHM.
  3. Read x = A sin(ωt+φ) as taughtThe motion.

3Simple harmonic motion and uniform circular motion

SHM as a shadow of uniform circular motion: a point on a circle of radius A, constant ω; the projection on a diameter is SHM. A = the circle’s radius; ω is the same turn-rate. The picture is a meaning, not a second law.

A circle-photo is a setting until the projection is named.

Figure. The NCERT link: a particle P that would ride a circle of radius A has a foot M on a diameter. That foot executes SHM, x = A\cos\omega t. This figure does not draw the circle — only the diameter, P at \omega t = 60^\circ (so x = A/2), and the dashed vertical drop to M. Cosine of 60° is one half, so M sits halfway from O to +A.

How it works

  1. Draw the circle and the diameterThe picture.
  2. Project; that coordinate is SHMThe link.
  3. Keep A and ω from the circleThe same numbers.

4Velocity and acceleration in simple harmonic motion

Velocity and acceleration in SHM: v = ±ω √(A²−x²), a = −ω² x as taught. At the end-point x=A, v=0 and |a| is max. At the mean, |v| is max and a=0. A max-speed at the end-point fails this pair.

Using v=ωx as if it were the end-point speed is a miss.

Figure. Both series share one scale: v/(A\omega)=-\sin\omega t (solid) and a/(A\omega^2)=-\cos\omega t (dashed). At t=0 the particle is at +A, so v=0 and acceleration is most negative (-\omega^2 A). A quarter period later v is most negative and a is zero — acceleration is -\omega^2 times displacement, not a second independent story. The mid-figure axis is the zero of both scaled quantities.

How it works

  1. Name x, A, ωThe given.
  2. Write v and a from the taught pairThe kinematics.
  3. Check ends versus meanThe extremes.

A=0.10 m, ω=10 rad/s, at mean

Find |v| and |a| at x=0.

  • |v|=ωA1.0 m/s
  • |a|=ω²x0
  • ReadFastest at the mean; a is 0 there

Pro tip. Ends: v=0, |a| max. Mean: opposite.

5Force law for simple harmonic motion

Force law for SHM: F = −k x with ω = √(k/m). A 0.4 kg on k=40 N/m has ω=10 rad/s. The minus is toward the mean. F is not a constant push.

Using F=k (no x) is a Hooke-half.

Figure. The SHM force law is F=-kx: through the origin, opposite in sign to x, and proportional. The solid line is that law (not to a newton scale — only the slope sign and the origin crossing are the claim). The dashed line is a constant restoring push. It is always leftward, so it is not proportional to x and the motion is not SHM.

How it works

  1. Name k and m (or F and x)The given.
  2. Write F=−kx and ω=√(k/m)The law.
  3. Keep the minusToward the mean.

6Energy in simple harmonic motion

Energy in SHM: E = ½ k A² = ½ m ω² A² stays (no friction). It splits as ½ kx² + ½ mv². At the end, all spring-store; at the mean, all K. A friction-swing leaks E.

Using ½ k x² as the total E at a mid-point is a miss.

Figure. Total mechanical energy E=\frac{1}{2}kA^2 is the same at every x (the dashed rule). At the mean, all of it is kinetic. At either extreme, all of it is potential. Midway in energy (x=A/\sqrt{2}, not A/2) the two shares are equal. The bar heights are shares of E, not a photograph of the spring.

How it works

  1. Write E = ½ k A²The total.
  2. Split into PE(x) and K(v)The trade.
  3. Keep E constant if the restore is idealThe conserve.

7The Simple Pendulum

A simple pendulum (small angle as taught) is SHM with T = 2π √(ℓ/g). A 1.0 m pendulum has T≈2.0 s if g=π² as a school convenience, or ~2.0 s at 9.8. T does not depend on mass or the small A. A large swing leaves this write.

Using T=2π√(g/ℓ) is the flip-steal.

Figure. A simple pendulum is a point mass on a light string of length L. For a small angle the restoring component is -mg\theta with \theta in radians, so the motion is SHM and T=2\pi\sqrt{L/g}. T does not depend on the bob mass or on how far you pulled it, once the angle stays small. The two string positions are a snapshot, not a drawn arc. \theta is about 18^\circ here so you can see it; the small-angle formula is already an approximation at that size.

How it works

  1. Name ℓ and gThe given.
  2. Write T=2π√(ℓ/g) for small anglesThe pendulum.
  3. Refuse a mass in the writeT independent of m.

8A definition is a test you can run

SHM / pendulum is a test: a ∝ −x, or T=2π√(ℓ/g). If you only say “swing”, you have a heading.

A playground-photo is not the test.

Figure. The chapter definition is a test you can run on a candidate force: does F stay proportional to -x through the origin for the displacements you were given? The solid line passes. A constant push (dashed) fails even though it always points toward the mean — restoring is not enough. If the test fails, do not call the motion SHM and do not write T=2\pi\sqrt{m/k}.

How it works

  1. Name a=−ω²x or the T-writeThe object.
  2. Give ω, T, or the energy-splitThe test.
  3. Then the word has contentThe definition ran.
At the SHM end-point, v is
  1. 0 — and |a| is max
  2. Max
  3. ωA always there too

Ends rest; mean is fastest.

Notes

  • Mapped to the official NCERT chapter “Oscillations”. Original teaching only — no textbook sentences.
  • Science here is Physics, Chemistry and Biology ideas at this class, never a language or social-science chapter.

Formulas

  • a=−ω²x
  • ω=√(k/m)
  • T=2π√(ℓ/g) (small pendulum)
  • E=½kA²

Recap

Hold these pegs from the official chapter “Oscillations”. The wording is ExamMaster’s teaching, not a textbook recap.

Periodic and oscilatory motions
Periodic motion repeats after a period T; oscillatory motion is a to-and-fro about a mean.
Simple harmonic motion
Simple harmonic motion: acceleration toward the mean, size ∝ displacement — a = −ω² x as taught.
Simple harmonic motion and uniform circular motion
SHM as a shadow of uniform circular motion: a point on a circle of radius A, constant ω; the projection on a diameter is SHM.
Velocity and acceleration in simple harmonic motion
Velocity and acceleration in SHM: v = ±ω √(A²−x²), a = −ω² x as taught.
Force law for simple harmonic motion
Force law for SHM: F = −k x with ω = √(k/m).
Energy in simple harmonic motion
Energy in SHM: E = ½ k A² = ½ m ω² A² stays (no friction).

Practise Oscillations

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