Playbook
Oscillations
110 q - 2.63/paper - 19% HARD. SHM kinematics is the biggest page, energy the cheapest; spring systems carry the HARD at 28%.
- Questions in the bank
- 110
- q/paper (2024–25 papers)
- 2.63
- Tagged HARD
- 19%
- Subtopics
- 4
Strand: Cornerstone
When you’ll see it
x = A sin(ωt + φ), a mass on a spring or springs, a pendulum (in a lift, on the Moon, or with a changed length), or energy shared between KE and PE.
How this chapter is tested
110 q at 2.63 a paper, 19% HARD. SHM Kinematics is the biggest page (44 q, 16%): v = ω√(A² − x²), a = −ω²x, and reading phase from the equation. SHM Energy is the cheapest (17 q, 12%): KE and PE trade places, and at x = A/√2 they are equal.
The HARD sits on Spring-Mass and Other SHM Systems (25 q, 28%): springs in series and parallel, a spring cut into pieces, a block between two springs. Stiffness adds in parallel and adds as reciprocals in series — the opposite of resistors — and a spring cut to 1/n of its length is n times stiffer.
The simple pendulum page (24 q, 21%) is T = 2π√(l/g) with an effective g: in a lift accelerating up, g + a; in free fall, zero, so the pendulum does not oscillate at all.
The sub-skills
The distinct skills inside the chapter, in the order to learn them.
SHM kinematics
v = ω√(A² − x²), a_max = ω²A, v_max = ωA. Read ω and φ straight from the equation.
SHM energy
E = ½kA². KE = PE at x = A/√2. At x = A/2, KE is three quarters of E.
Spring combinations
Parallel: k = k₁ + k₂. Series: 1/k = 1/k₁ + 1/k₂. T = 2π√(m/k). A spring's k ∝ 1/length.
Pendulum with an effective g
T = 2π√(l/g_eff). Lift up: g + a; down: g − a; free fall: T infinite.
Traps to expect
Distractor shapes this chapter reuses. The Traps page covers the patterns that cut across chapters.
Treating springs like resistors
Springs in PARALLEL add their constants directly (stiffer); in series they add as reciprocals. It is the reverse of resistors.
Halving the energy at half the amplitude
PE ∝ x², so at x = A/2 the PE is a QUARTER of the total and the KE three quarters. Linear thinking gives half-and-half.
Learn it before you drill it
This chapter has full teaching notes — foundations, worked examples, self-checks and a per-subtopic mastery checkpoint. Read the notes once, then drill subtopic by subtopic below.
Oscillations notesDrill every oscillations question
110 questions from the bank, scoped to 4 bundled subtopics.
Drill one subtopic at a time
The 4 subtopics this playbook covers, in catalog order.
Related playbooks
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