Chapter 13 — Oscillations

Chapter 13 of the Class 11 Physics NCERT textbook, "Oscillations", covers periodic motion in which objects move back and forth about an equilibrium position, with displacement described by sinusoidal functions like x(t) = A cos(ωt + φ) in simple harmonic motion.

• Simple harmonic motion — Among oscillatory motions, SHM is the simplest, with sinusoidal displacement about an equilibrium point. It is characterised by amplitude, angular frequency, phase, period, and frequency, which together fully describe the repeating motion.
• Circular-motion connection and restoring force — SHM can be seen as the projection of uniform circular motion onto a diameter, giving geometric insight. Its defining feature is a restoring force always directed toward equilibrium, proportional to displacement.
• Energy exchange and the pendulum — In SHM, energy shifts continually between kinetic and potential forms while the total stays constant. The simple pendulum realises SHM for small swings, with a period depending only on length and gravity, not amplitude or mass.

1. 01Periodic motion repeats at regular intervals; oscillatory motion is to-and-fro about equilibrium with an equilibrium position where no net force acts
2. 02Simple harmonic motion (SHM) has displacement x(t) = A cos(ωt + φ) where amplitude A is maximum displacement, angular frequency ω = 2π/T, and phase constant φ determines initial conditions
3. 03Velocity v(t) = –ωA sin(ωt + φ) and acceleration a(t) = –ω²x(t) in SHM; both are periodic with period T/2 for velocity magnitude and T for displacement
4. 04Force in SHM is restoring: F = –kx = –mω² x, always directed toward equilibrium; k = mω² relates spring constant to mass and angular frequency
5. 05Energy in SHM conserves total mechanical E = ½kA² = K + U; kinetic energy peaks at equilibrium, potential energy peaks at maximum displacement
6. 06Simple pendulum for small angles executes SHM with period T = 2π√(L/g), independent of amplitude or mass