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Oscillations
Physics · Class 11NCERT pp. 259–2722 sets × 25 questions
Key facts and formulas for Oscillations, three worked sample questions, and two full practice sets. Every question has a hint, a reason for every option and a step-by-step solution, with a calculator or animation where one helps. English and Hinglish.
Formula sheet for this chapter
| Idea | Rule or fact |
|---|
| Period, frequency, ω | T = 1/ν, ω = 2π/T = 2πν |
| SHM displacement and speed | x = A sin(ωt + φ), v = ω√(A² − x²), vmax = ωA |
| Acceleration | a = −ω²x, amax = ω²A, velocity leads displacement by π/2 |
| Spring-mass system | T = 2π√(m/k), k = mω², parallel k = k₁ + k₂, series 1/k = 1/k₁ + 1/k₂ |
| Energy in SHM | E = ½kA², K = ½k(A² − x²), U = ½kx², K and U repeat every T/2 |
| Simple pendulum | T = 2π√(L/g), independent of mass, T ∝ √L, T ∝ 1/√g |
| Effective g | Lift up: g + a; lift down: g − a; horizontal a: √(g² + a²) |
| Physical pendulum and liquids | T = 2π√(I/mgd); U-tube T = 2π√(l/2g); floating body k = Aρg |
| Superposition | A = √(A₁² + A₂² + 2A₁A₂ cos φ); damping: A = A₀e^(−bt/2m); resonance at ν = ν₀ |
Three sample questions
Q1. Which of the following motions is periodic but not oscillatory?
- A pendulum bob swinging through a small angle
- A block on a spring moving to and fro
- A particle in uniform circular motion
- A piston moving in a cylinder
Hint and solution
Hint: Oscillatory motion needs a to and fro movement about a mean position. Which motion repeats but never goes back and forth?
- Periodic = repeats; oscillatory = to and fro — Periodic motion repeats after a fixed time. Oscillatory motion also needs a to and fro movement about a mean position.
- Pendulum, spring block, piston: all go to and fro — These three move back and forth about a central point, so they are periodic and oscillatory.
- Circular motion: repeats, no to and fro — A particle in uniform circular motion returns to the same point each revolution but does not oscillate about any point.
- Answer: circular motion — So the motion that is periodic but not oscillatory is uniform circular motion. Option C.
Answer: C. The circular motion repeats, but there is no to and fro about a point where the force is zero. The others oscillate about a mean position.
Q2. Statement I: Every oscillatory motion is periodic. Statement II: Every periodic motion is oscillatory. Choose the correct option.
- Statement I is true and Statement II is false
- Both statements are true
- Statement I is false and Statement II is true
- Both statements are false
Hint and solution
Hint: Test each statement with an example. Is a planet going round the Sun periodic? Does it go to and fro about a point?
- Oscillatory ⊂ periodic — Oscillation repeats after a fixed time, so Statement I is true.
- Test II with a planet — A planet in orbit repeats every year, so it is periodic, but it has no to and fro motion about an equilibrium point.
- II is false — One counter example is enough, so Statement II fails.
- Answer: I true, II false — So the correct choice is: Statement I is true and Statement II is false. Option A.
Answer: A. Oscillation repeats at equal gaps, so it is periodic. A planet in orbit is periodic but has no to and fro motion about an equilibrium point.
Q3. A source vibrates with a period of 0.04 s. Its frequency in hertz is
- 0.25
- 2.5
- 250
- 25
Hint and solution
Hint: Frequency is the number of vibrations per second, the inverse of the period.
- ν = 1/T — Frequency is the reciprocal of the time period.
- ν = 1 / 0.04 s — Put the given period T = 0.04 s into the formula.
- 1 ÷ 0.04 = 25 — Dividing 1 by 0.04 gives 25 per second.
- ν = 25 Hz — So the frequency is 25 hertz. Option D.
Answer: D. ν = 1/T = 1/0.04 = 25 Hz.
How to use this chapter
Read the NCERT pages first, then attempt Set 1 without the hints. Note every wrong answer in a mistake list, read the reason for each option, and retry Set 2 two days later. A topic is solid when you can say why each wrong option is wrong.