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Playbook

Oscillations and Waves

13 q · 15% HARD. Simple pendulum T=2π√(L/g) (period-vs-length-vs-mass-vs-g ratios), SHM displacement/velocity/acceleration sign mapping, wave property statements. Small chapter, formula-rich.

questions in the bank
13
tagged HARD
15%
subtopic(s)
2
worked examples
2

When you’ll see it

A pendulum period change with L / mass / g, a SHM displacement-velocity-acceleration sign mapping, or a 'do EM, sound, water waves all carry energy' statement-truth.

How this chapter is tested

13 q in 10 years · 15% HARD. Two subtopics: Simple Pendulum (7 q) and SHM + General Waves (6 q). Small chapter, formula-rich.

T_pendulum = 2π√(L/g). The most-tested fact: mass DOESN'T appear. Doubling mass changes nothing. Doubling L multiplies T by √2 ≈ 1.41. Moving to a planet with g/4 doubles T. The recurring shape: 'L increased 4×, m doubled, find new T/old T' — answer is √4 = 2, mass irrelevant.

SHM: displacement x = A sin(ωt), velocity v = Aω cos(ωt), acceleration a = −Aω² sin(ωt) = −ω²x. Acceleration is OPPOSITE in sign to displacement (always pointing toward equilibrium). At extremes (x = ±A), v = 0, a = max. At equilibrium (x = 0), v = max, a = 0.

The sub-skills

The rules and habits that decide whether you get a question right.

  • Pendulum period ratio

    T = 2π√(L/g). Doubling L multiplies T by √2. Halving g multiplies T by √2. Mass irrelevant. Air resistance only affects amplitude over time, not period (to first approximation).

  • SHM x-v-a sign mapping

    x and a always OPPOSITE sign. v is 90° (¼-cycle) ahead of x. At extremes: v=0, a=max. At equilibrium: v=max, a=0.

  • Wave general properties

    All waves (EM, sound, water) carry energy; exhibit reflection, refraction, diffraction, superposition. Sound and water need a medium; EM doesn't (can travel in vacuum).

2 worked examples from the bank

Real past-year questions illustrating the playbook. Click to reveal options + solution.

Example 1Oscillations and WavesMODERATE
The length of a simple pendulum is increased four times to its previous value while the mass is doubled. What is the ratio of the new and previous time period of the pendulum?

[Q134 · Apr · 2025]

Example 2Oscillations and WavesMODERATE
A pendulum of length LL oscillates with an angular amplitude of θ=60°\theta = 60° and time period TT. Let T0=2πLgT_0 = 2\pi\sqrt{\frac{L}{g}} be the time period for small angle oscillations. If air resistance is negligibly small and the string remains straight, then which one of the following is correct?

[Q51 · Apr · 2026]

Traps to expect

Distractor shapes specific to this chapter. The page-wide Traps section covers the bank-level patterns.

  • Mass in pendulum period

    Mass doesn't appear. 'When mass doubles, period doubles' is the standard wrong option. Same trap: 'air resistance changes the period' — air resistance damps the AMPLITUDE, not the period.

  • Direction of acceleration in SHM

    Acceleration is OPPOSITE to displacement, always pointing toward equilibrium. Wrong option says 'acceleration is in the direction of motion' (only true on the way back to equilibrium, not the way out).

Drill every oscillations and waves question

13 questions from the bank, scoped to 2 bundled subtopics.

Drill the 13 questions

Related playbooks

Often paired with this one — drill these next if you found the worked examples above tractable.