Tamil Nadu Class 11 Physics Oscillations — Samacheer Kalvi Plus One

Quick Summary

Oscillations are the basis of wave motion, sound, and electromagnetic radiation. SHM is the simplest oscillatory motion and a key topic for NEET (always 1–2 questions) and for understanding wave physics.

Simple Harmonic Motion (SHM)

A body executes SHM if its acceleration is proportional to displacement and directed toward equilibrium:

F = −kx → a = −ω²x

Equations of SHM

• Displacement: x = A sin(ωt + φ) or A cos(ωt + φ)
• Velocity: v = Aω cos(ωt + φ) = ω√(A² − x²)
• Acceleration: a = −Aω² sin(ωt + φ) = −ω²x

Angular frequency: ω = 2π/T = 2πf

At mean position: displacement = 0, velocity = maximum (Aω), acceleration = 0

At extreme position: displacement = A, velocity = 0, acceleration = maximum (ω²A)

Time Period Formulae

Energy in SHM

• Kinetic energy: KE = ½mω²(A² − x²)
• Potential energy: PE = ½mω²x²
• Total energy: E = ½mω²A² = ½kA² (constant)

At mean position: KE = max, PE = 0

At extreme position: KE = 0, PE = max

Types of Oscillations

Important Questions

One Mark

• Define SHM.
• Write the time period of a simple pendulum.
• At which position is velocity maximum in SHM?
• What is resonance?
• Write the formula for total energy in SHM.

Short Answer (3 marks)

• Derive the expression for total energy in SHM. Show that it is constant.
• Show that the motion of a mass on a spring is SHM and derive the expression for time period.
• Explain damped oscillations and their significance.

Long Answer (5 marks)

• Define SHM. Write equations for displacement, velocity, and acceleration. Discuss the variation of KE and PE with displacement and time. Sketch the energy graphs.
• Explain forced oscillations and resonance. Give three practical examples of resonance (useful and harmful).

Common Mistakes

• Using T = 2π√(m/g) for spring instead of 2π√(m/k).
• Forgetting that time period of a simple pendulum is independent of mass AND amplitude (for small angles only).
• Calculating velocity as Aω everywhere — it equals Aω only at mean position.

Board Exam Tips

• Energy in SHM (KE, PE, total) is a standard 5-mark derivation.
• Spring-mass and pendulum period problems appear as short numericals.
• NEET: Phase difference, velocity and acceleration expressions, and energy are common MCQ topics.