PYQ Vault

Playbook

Oscillations

Simple harmonic motion, springs and pendulums. Lighter than in the early papers; time-period questions dominate.

Questions in the bank
120
q/paper in 2025–26
0.68
Numeric answer
32%
Notes pages
5

Tier: Long tail

When you’ll see it

A body moving to and fro about a mean position: an SHM equation, the period of a spring or pendulum, the energy at a displacement, or a new amplitude after a push.

How this chapter is tested

Oscillations sits in the long tail and has shrunk on the recent papers, but many of its questions ask for a number. Nearly all of it is simple harmonic motion, and almost every question comes down to two numbers, ω and the amplitude, from which a phase, a time, a speed or an energy follows in a line or two.

The harder step is finding ω for a new set-up: a cut spring, a block between two springs, two free masses, a physical pendulum, a lift, a height above the earth. Write the restoring force per unit displacement, divide by the mass, and the rest is the standard SHM page.

Marks are lost on a factor: springs read as series when they act in parallel, half the amplitude taken as half the time, or a height R taken as a distance R from the centre. The effective-g ideas come from Gravitation, the physical pendulum from Rotational Motion, and the same sine equation returns in Waves.

The sub-skills

The distinct skills inside the chapter, in the order to learn them.

  • The SHM equation

    Read the phase in x = A sin(ωt + φ), choose the initial phase by the starting direction, and use v = ω√(A² − x²) and a = −ω²x.

  • Timing and combining SHMs

    The time between two positions is the phase covered divided by ω; two SHMs of one frequency on a line add as vectors; two different frequencies never make SHM.

  • Springs and restoring forces

    ω² = force per unit displacement ÷ mass: a cut spring is stiffer, a block between walls is parallel, two free masses use the reduced mass, a physical pendulum uses I about the pivot.

  • Simple pendulum and effective g

    T = 2π√(L/g) whatever the bob's mass; a height, a planet, a lift or a liquid changes only the g in that formula.

  • Energy, amplitude changes and damping

    Total energy ½kA²; kinetic equals potential at A/√2; a mass added at the mean shares momentum and lowers the amplitude; damped energy decays twice as fast as amplitude.

Traps to expect

Distractor shapes this chapter reuses. The Traps page covers the ones that cut across chapters.

  • A block between two walls read as series

    Springs on opposite sides of a block look like a chain, but both stretch by the same x and both push back, so k = k₁ + k₂.

  • Equal distances in equal times

    Mean to A/2 takes T/12, but A/2 to the extreme takes T/6, because the particle slows down near the extreme.

  • A height R read as a distance R

    At a height equal to the earth's radius the distance from the centre is 2R, so g falls to a quarter and the period doubles.

  • Equal energies at half the amplitude

    At A/2 the potential energy is only a quarter of the total. Kinetic and potential energy are equal at A/√2.

Learn it before you drill it

This chapter has full teaching notes — foundations, worked examples, self-checks and a mastery check for each page. Read the notes once, then drill page by page below.

Oscillations notes

Drill every Oscillations question

120 questions from the bank, across 5 subtopics.

Drill the 120 questions

Drill one subtopic at a time

The 5 subtopics, in teaching order.

Related playbooks

Often paired with this one — the technique or the trap overlaps. Drill these next.