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Class 11 Physics Notes

Oscillations Class 11 Physics Notes

Complete, exam-ready notes on oscillations: periodic motion, simple harmonic motion (SHM), the spring-mass and simple pendulum systems, energy in SHM, and damped and forced oscillations — written for CBSE, JEE and NEET revision.

Class11SubjectPhysicsCoversCBSE · JEE · NEET

Written byDeep Narayan· Science & Mathematics EducatorReviewed byPushpanjali

What is simple harmonic motion in one line?

Simple harmonic motion is periodic motion in which the restoring force is directly proportional to the displacement and opposite in direction, so the acceleration is proportional to displacement: a = −ω²x.

Periodic Motion and SHM Basics

Simple harmonic motion

a=−ω2xa = -\omega^2 x

A particle executing SHM has acceleration proportional to and opposite the displacement. Its position varies sinusoidally: x(t)=Acos⁡(ωt+ϕ)x(t) = A\cos(\omega t + \phi), where A is amplitude, ω angular frequency and φ the phase constant.

  • Period T = 2π/ω; frequency f = 1/T = ω/2π.
  • Velocity:
  • v=±ωA2−x2v = \pm\omega\sqrt{A^2 - x^2}
  • — maximum at mean position, zero at extremes.
  • Acceleration is maximum at extremes, zero at mean position.
x=Acos⁡(ωt+ϕ),v=±ωA2−x2x = A\cos(\omega t+\phi),\quad v = \pm\omega\sqrt{A^2-x^2}
SHM displacement and velocity

Spring-Mass System and Simple Pendulum

Spring-mass period

T=2πmkT = 2\pi\sqrt{\frac{m}{k}}

For a mass m on a spring of spring constant k, the angular frequency is ω=km\omega = \sqrt{\frac{k}{m}}. The period is independent of amplitude.

Simple pendulum period

T=2πLgT = 2\pi\sqrt{\frac{L}{g}}

For small oscillations, the period of a simple pendulum depends only on its length L and gravitational acceleration g — not on the mass or amplitude.

ωspring=km,ωpendulum=gL\omega_{\text{spring}} = \sqrt{\frac{k}{m}},\quad \omega_{\text{pendulum}} = \sqrt{\frac{g}{L}}
Angular frequencies

Rise in g lowers period

A pendulum's period decreases at higher altitude-independent places with larger g (e.g. moving from equator to pole it runs slightly faster because g increases).

Energy in SHM

  • Total energy is constant and proportional to A²:
  • E=12mω2A2E = \frac{1}{2}m\omega^2 A^2
  • .
  • Kinetic energy:
  • K=12mω2(A2−x2)K = \frac{1}{2}m\omega^2(A^2 - x^2)
  • .
  • Potential energy:
  • U=12mω2x2U = \frac{1}{2}m\omega^2 x^2
  • .
  • Kinetic energy is maximum at the mean position; potential energy is maximum at the extremes.
E=12kA2,K+U=E (constant)E = \frac{1}{2}kA^2,\quad K + U = E\ \text{(constant)}
Energy in SHM

Damped and Forced Oscillations

  • Damped oscillations lose energy to friction/drag; amplitude decays exponentially over time.
  • Forced oscillations occur when a periodic driving force is applied; amplitude depends on the driving frequency.
  • Resonance is a sharp rise in amplitude when the driving frequency equals the natural frequency (e.g. a swing pushed at its natural rhythm).

Amplitude at resonance

At resonance the amplitude becomes large; without damping it can grow indefinitely. Damping broadens the resonance peak and lowers its height.

Solved Examples

Example: A pendulum of length 2 m2\,\text{m} swings with small amplitude at a place where g=9.8 m/s2g = 9.8\,\text{m/s}^2. Find its period.

Solution: T=2πLg=2π29.8≈2×3.14×0.45≈2.8 sT = 2\pi\sqrt{\frac{L}{g}} = 2\pi\sqrt{\frac{2}{9.8}} \approx 2\times3.14\times0.45 \approx 2.8\,\text{s}.

Revision

Key formulas at a glance

Memorise these before attempting numericals — most exam questions hinge on one of them.

SHM condition

a=−ω2xa = -\omega^2 x

Period

T=2πωT = \frac{2\pi}{\omega}

Spring period

T=2πmkT = 2\pi\sqrt{\frac{m}{k}}

Pendulum period

T=2πLgT = 2\pi\sqrt{\frac{L}{g}}

Total energy

E=12kA2E = \frac{1}{2}kA^2

SHM velocity

v=±ωA2−x2v = \pm\omega\sqrt{A^2-x^2}

Exam tips

How this chapter is asked

Where this topic appears in CBSE, JEE Main and NEET papers.

  • In SHM, a = −ω²x.
  • Spring period T = 2π√(m/k); pendulum T = 2π√(L/g).
  • Total energy ∝ A²; KE max at mean position.
  • Amplitude decays exponentially in damped oscillations.
  • Resonance at driving frequency = natural frequency.

FAQ

Common questions

What is simple harmonic motion?

Periodic motion where the restoring force is proportional to displacement and opposite in direction, so acceleration a = −ω²x and displacement varies sinusoidally.

Why does a pendulum's time period not depend on mass?

Mass cancels because both the restoring force and inertia depend on mass; the period depends only on length and g: T = 2π√(L/g).

What is resonance?

A sharp increase in amplitude when the driving frequency matches the natural frequency of the system, allowing maximum energy absorption.

What happens to energy in damped oscillations?

Energy is gradually lost to friction or drag, so the amplitude decays exponentially until the oscillation stops.

Continue learning

Related notes

All Class 11 NotesClass 11 Units and Measurements NotesClass 11 Laws of Motion NotesPhysics Tutor in Mohali

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