NCERT Solutions for Class 11 Physics Chapter 14 – Oscillations
Chapter 14 of Class 11 Physics, Oscillations, introduces students to repetitive, to-and-fro motion — one of the most ubiquitous phenomena in nature and technology. From the swinging of a pendulum clock to the vibrations of atoms in a crystal, oscillatory motion follows universal mathematical patterns. The chapter focuses primarily on Simple Harmonic Motion (SHM), a special type of periodic motion where the restoring force is directly proportional and opposite to displacement: F = −kx. This leads to sinusoidal motion described by x(t) = A cos(ωt + φ). Students learn to derive equations for displacement, velocity, and acceleration in SHM and compute the kinetic energy, potential energy, and total mechanical energy at any instant. Two canonical systems are studied in depth: the spring-mass system (horizontal and vertical) and the simple pendulum (for small angles).
The chapter then extends to damped oscillations — where energy is lost due to friction or drag — and forced oscillations — where an external periodic force is applied. The critical phenomenon of resonance, when the driving frequency matches the natural frequency, explains structures collapsing, musical instruments, and MRI machines. This chapter is a favourite in JEE Advanced and forms the backbone of wave theory in Chapter 15.
NCERT Solutions PDF – Class 11 Physics Chapter 14 (All Exercises)
Important Formulas – Chapter 14: Oscillations
| Formula | Expression | Description |
|---|---|---|
| SHM Restoring Force | F = −kx | k = spring constant or effective constant; negative = restoring |
| Displacement in SHM | x(t) = A cos(ωt + φ) | A = amplitude; ω = angular frequency; φ = initial phase |
| Angular Frequency | ω = 2π/T = 2πf = √(k/m) | For spring-mass system |
| Velocity in SHM | v = −Aω sin(ωt + φ); v_max = Aω | Max speed at equilibrium (x=0) |
| Acceleration in SHM | a = −ω²x; a_max = ω²A | Max acceleration at extreme positions |
| Time Period (Spring-Mass) | T = 2π√(m/k) | Independent of amplitude; m = mass, k = spring constant |
| Time Period (Simple Pendulum) | T = 2π√(L/g) | Valid for small angles (θ < 15°); independent of mass |
| Kinetic Energy in SHM | KE = ½mω²(A²−x²) | Maximum at x = 0; zero at x = ±A |
| Potential Energy in SHM | PE = ½mω²x²= ½kx² | Minimum at x = 0; maximum at x = ±A |
| Total Energy | E = ½mω²A² = ½kA² | Constant in undamped SHM; independent of x |
| Velocity-displacement | v = ω√(A²−x²) | Useful for finding speed at any position |
| Damped Oscillation | x = Ae^(−bt/2m) cos(ω't + φ) | Amplitude decreases exponentially; ω' = √(ω²−b²/4m²) |
Subtopics Explained – Chapter 14: Oscillations
Periodic and Oscillatory Motion
Periodic motion repeats after a fixed time interval (period T). Oscillatory motion is periodic motion about a fixed equilibrium position. All oscillatory motion is periodic, but not vice versa (e.g., Earth's revolution is periodic but not oscillatory). SHM is the simplest and most important type of oscillatory motion.
Simple Harmonic Motion (SHM)
SHM is defined by a linear restoring force: F = −kx. The solution is sinusoidal. At amplitude ±A, velocity is zero and acceleration is maximum. At equilibrium (x = 0), velocity is maximum (v_max = Aω) and acceleration is zero. Understanding these phase relationships is critical for solving NCERT problems efficiently.
Spring-Mass System
For a mass m on a spring of constant k, T = 2π√(m/k). For a vertical spring, the equilibrium shifts by mg/k but the time period remains the same. For springs in series, k_eff = k₁k₂/(k₁+k₂); for parallel, k_eff = k₁+k₂. These spring combinations are frequent exam topics.
Simple Pendulum
A simple pendulum (point mass on inextensible string) executes SHM for small angles, with T = 2π√(L/g). The period is independent of mass and amplitude (for small angles) — a key property. The pendulum can be used to determine g experimentally. Seconds pendulum has T = 2 s, so L ≈ 1 m for standard g.
Damped and Forced Oscillations
In damped oscillations, resistive forces reduce amplitude over time. The system is underdamped (oscillates with decreasing amplitude), critically damped (returns to equilibrium fastest without oscillation), or overdamped (slowly returns). In forced oscillations, an external periodic force is applied. When its frequency matches the system's natural frequency, resonance occurs — amplitude becomes very large, which is both useful (MRI, musical instruments) and dangerous (bridge collapses).
| Resource Name | Description | Best For |
|---|---|---|
| NCERT Solutions | Detailed answers and explanations for NCERT textbook questions across all classes and subjects. | Homework, assignments, and exam preparation |
| NCERT Solutions for Class 11 | Chapter-wise solutions for all Class 11 subjects including Physics, Chemistry, Mathematics, Biology, and English. | Class 11 board exam preparation |
| NCERT Solutions for Class 11 Physics | Step-by-step solutions covering all chapters such as Motion, Laws of Motion, Work Energy and Power, Thermodynamics, and Waves. | Concept building and numerical problem-solving |
| NCERT Exemplar Class 11 Physics | Advanced and application-based questions designed to strengthen conceptual understanding and analytical skills. | JEE, NEET, Olympiads, and higher-order practice |
| Physics Formula | Chapter-wise collection of important formulas, equations, and derivations for quick revision. | Last-minute revision and numerical practice |
Quick Reference Table – Key Comparisons in Oscillations
| System | Time Period | Depends On | Does NOT Depend On |
|---|---|---|---|
| Spring-Mass | 2π√(m/k) | Mass m, spring constant k | Amplitude, g |
| Simple Pendulum | 2π√(L/g) | Length L, gravity g | Mass, amplitude (small) |
| Liquid in U-tube | 2π√(L/2g) | Length of liquid column L | Mass, density |
| Torsional Pendulum | 2π√(I/C) | Moment of inertia I, torsion C | Amplitude |
| SHM Energy | E = ½kA² | Amplitude A, spring constant k | Mass, position x |