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SS2 Physics · WAEC · NECO · JAMB · Paper 3 Practical

Simple Harmonic Motion: The Cracked Crates of Ridge Road

Dayo’s okada carries Hajia Ramatu’s eggs over the same row of drainage ridges every morning. At a crawl the trays survive; at a brisk pace they survive; but at one in-between speed the back of the bike pumps up and down until the crates leap off the carrier and crack. Time a bounce, pull a spring, swing a pendulum, measure g in your own lab, and work out the exact speed Dayo must never ride.

Begin Lesson 1 →
Scope
7 lessons · ~9 h 20 min
Interactive
7 virtual labs + 7 zooms
Practice
84 quiz questions + 7 × 30-mark papers
Practical
Paper 3: pendulum T²–l, loaded spring
LIVE 3D LAB · MRS OKAFOR’S BENCH & RIDGE ROAD
Drag to turn · Tap a part
x₀ = mg/k8.0 cm
T = 2π√(m/k)0.568 s
f = 1/T1.76 Hz
ω = 2π/T11.1 rad/s

Add load or change the spring, then tap Pull & release.

01 / The Phenomenon

Slow is safe, fast is safe, but one speed breaks the eggs.

Every lesson in this unit closes one piece of the same case file, from a bouncing okada outside Ogbomoso to a pendulum on Mrs Okafor’s lab bench.

The Unit Mystery · Ridge Road, Ogbomoso

The Cracked Crates of Ridge Road

Outside Ogbomoso, Hajia Ramatu packs trays of eggs into crates every dawn, and Dayo rides them to the town market on his okada. Halfway there, the laterite road crosses a run of low concrete drainage ridges laid by the council, all about the same distance apart.

Her daughter Zainab, an SS2 student, keeps a notebook of the losses, and the pattern is strange: slow trips are fine, fast trips are fine, but trips at one middle speed end in broken eggs. Her classmate Tunde is sure that faster always means worse. Their physics teacher, Mrs Okafor, says the bike is behaving like a mass on a spring, and that physics can name the dangerous speed before another tray is lost.

Why does one in-between speed throw the crates off, and what must Dayo and Mallam Sule change?

  • Clue 1Crates arrive whole at 10 km/h and at 30 km/h.
  • Clue 2Crates crack at about 18 km/h.
  • Clue 3With two extra crates, the bad speed falls to about 16 km/h.
  • Clue 4Mallam Sule finds the rear shock absorber weeping oil.

Realism note: story numbers are a teaching model: chosen to be realistic and easy to work with, not measured on a real okada or road. (Teachers: 200 kg on the rear spring, a 2 Hz bounce, ridges 2.5 m apart; real suspensions and roads vary.)

Papers 1–3
Marks at stake SHM theory and the pendulum practical keep coming back across WAEC and NECO papers
3 boards
WAEC · NECO · JAMB Period ratios, x–v–a relations and resonance are favourite objective questions
3 laws
Core laws a = −ω²x · T = 2π√(l/g) · resonance f = f₀
02 / Your Learning Journey

Seven lessons, one bouncing okada, from a stopwatch to the dangerous speed.

Each lesson takes about 80 minutes with a movement break, opens with a Do Now warm-up, and walks you through a 3D story, a virtual practical, a zoom, worked examples and a WAEC-style quiz.

01

Things That Repeat

80 min · Live

Put a number on a bounce: period, frequency and angular frequency, timed the examiner’s way.

periodic timing practical Start lesson →
02

The Pull Back to the Middle

80 min · Live

Restoring force, the SHM condition and the loaded spring: why extra crates slow the bounce.

Hooke T = 2π√(m/k) graph Start lesson →
03

SHM as a Circle’s Shadow

80 min · Live

When exactly do the crates leave the carrier? Displacement, velocity and acceleration, and the lift-off rule.

x, v, a reference circle 2D Start lesson →
04

The Simple Pendulum

80 min · Live

Does a heavier bob or a bigger swing change the timing? Fair tests, small angles and T = 2π√(l/g).

T = 2π√(l/g) ratios myths Start lesson →
05

WAEC Practical: Finding g

80 min · Live

The Paper 3 pendulum, end to end: split cork, composite table, the T²–l graph and the precautions.

Paper 3 T²–l graph precautions Start lesson →
06

Energy in SHM and Damping

80 min · Live

Where does the bounce energy go? Kinetic and potential energy, and what a shock absorber is for.

KE ⇄ PE ½kA² shock absorber Start lesson →
07

Forced Vibration and Resonance

80 min · Live

Solve the Ridge Road case: Barton’s pendulums, f = v/d, and the verdict for Dayo and Hajia Ramatu.

Barton’s pendulums f = v/d verdict Start lesson →

Built-in spaced retrieval: every lesson’s Do Now pulls cards from earlier lessons, and every lesson hands Zainab one more clue. By Lesson 7 you have the period, the spring constant, the lift-off rule, the local g and the damping story needed to name the dangerous speed.

03 / Interactive Sneak Preview

Five graphs that explain the whole unit.

Tap a tab, then slide along the graph. You will meet every one of these again in a lesson, with your own readings.

x, v and a against time

Lesson 3 bench: A = 0.30 m, T = 2.0 s (the mud lump’s shadow)

The rule
x = A sin ωt · v = ωA cos ωt · a = −ω²x
Shape of the graph
v runs a quarter-cycle ahead of x; a is x upside down
Exam point
Speed peaks where x = 0; acceleration peaks at the ends

Slide through one cycle. Wherever the amber x curve crosses zero, the teal v curve is at a peak: the body is fastest in the middle. At the ends v is zero but the dashed a curve is at its biggest, pointing back to the centre.

04 / Learning Outcomes

What you will master by the end of Lesson 7.

Every skill is practised on a virtual bench, seen up close in a zoom and tested with WAEC, NECO and JAMB-style questions.

01

Measure an oscillation

Classify periodic and oscillatory motion and find T, f and ω from timing data.

02

State the SHM condition

Use Hooke’s law and a = −ω²x: acceleration proportional to displacement, always towards the centre.

03

Use x, v and a

Apply x = A sin ωt, v = ω√(A² − x²) and a_max = ω²A, and say where each peaks.

04

Use both period formulas

Solve ratio problems with T = 2π√(m/k) and T = 2π√(l/g).

05

Find g in the lab

Carry out the Paper 3 pendulum, plot T² against l and deduce g = 4π²/slope.

06

Explain energy and resonance

Use E = ½kA², explain damping, and predict a resonant speed with v = d f₀.

The 6 calculation archetypes

Almost every number question on simple harmonic motion in WAEC, NECO and JAMB is one of these six. Each step has a note under it.

Type 1 · Lesson 1

Timing an oscillation

  1. T = t/n = 10.0 ÷ 20 = 0.50 sZainab counts 20 bounces of the parked okada in 10.0 s.
  2. f = 1/T = 1 ÷ 0.50 = 2.0 HzFrequency is the reciprocal of the period.
  3. ω = 2πf = 2 × 3.142 × 2.0 = 12.6 rad s⁻¹Angular frequency is 2π times the frequency.
Type 2 · Lesson 3

SHM kinematics

  1. v = ω√(A² − x²) = 5.0√(0.010 − 0.0036)A = 0.10 m, ω = 5.0 rad s⁻¹, at x = 0.060 m.
  2. v = 5.0 × 0.080 = 0.40 m s⁻¹The square root of 0.0064 is 0.080.
  3. a = −ω²x = −25 × 0.060 = −1.5 m s⁻²The minus sign: the acceleration points back to the centre.
Type 3 · Lesson 2

The loaded spring

  1. k = F/x = (0.30 × 9.8) ÷ 0.060 = 49 N m⁻¹A 0.30 kg load stretches the spring by 6.0 cm.
  2. T = 2π√(m/k) = 2π√(0.30 ÷ 49) = 0.49 sMore mass gives a longer period; a stiffer spring a shorter one.
  3. k = 4π²/slope = 39.48 ÷ 1.61 = 24.5 N m⁻¹From the gradient of a T² against m graph.
Type 4 · Lesson 4

The simple pendulum

  1. T = 2π√(l/g) = 2π√(0.90 ÷ 9.8) = 1.90 sOnly the length and gravity count, for small swings.
  2. T₂/T₁ = √(l₂/l₁) = √(0.90 ÷ 0.40) = 1.5A ratio problem: the 1.27 s pendulum becomes 1.90 s.
  3. l = gT²/4π² = (9.8 × 2.0²) ÷ 39.5 = 0.99 mThe seconds pendulum: a period of 2.0 s.
Type 5 · Lesson 5

Practical g from a graph

  1. s = (4.032 − 1.613) ÷ (1.000 − 0.400) = 4.03 s² m⁻¹Slope of the T² against l line from a large triangle.
  2. g = 4π²/s = 39.48 ÷ 4.03 = 9.79 m s⁻²Our class value for g.
  3. H = 1.80 + 4.028 ÷ 4.03 = 2.80 mCeiling variant: the T² against y line meets the axis at the ceiling height.
Type 6 · Lessons 6–7

Energy and resonance

  1. E = ½kA² = ½ × 50 × 0.10² = 0.25 JTotal energy depends on the amplitude squared.
  2. KE = E − ½kx² = 0.25 − 0.090 = 0.16 JAt x = 0.060 m, the rest of the energy is kinetic.
  3. v = d f₀ = 2.5 × 2.0 = 5.0 m s⁻¹ = 18 km h⁻¹The ridges push at the natural frequency: resonance.
a = −ω²xSHM condition
ω = 2πfAngular frequency
v = ω√(A² − x²)Speed at x
T = 2π√(m/k)Loaded spring
T = 2π√(l/g)Simple pendulum
E = ½kA²Total energy
f = f₀Resonance

Three myths we will bust

Tap each card to flip it and see the physics:

05 / How Every Lesson Works

Measure it first, then explain it.

After a short Do Now warm-up, every lesson follows the same five-step inquiry loop, with a movement break at 45 minutes, so you test an idea before you memorise it.

  1. 1 · Wonder

    Watch the 3D story and pin your prediction

    Zainab, Tunde, Dayo, Hajia Ramatu, Mallam Sule and Mrs Okafor meet a real puzzle. Post your guess on the Wonder Wall.

  2. 2 · Investigate

    Sort, then work the virtual practical

    Time oscillations, load a spring, swing a pendulum, ride the ridges, and plot the readings live.

  3. 3 · Make sense

    Zoom in and build the rules

    See restoring forces, a circle’s shadow, a cut-away shock absorber and a resonance curve, then write the rules.

  4. 4 · Apply

    Worked examples, the Bridge and a quiz

    Step-by-step calculations, a case-solving challenge and 12 exam-style questions every lesson.

  5. 5 · Reflect

    Rate yourself and unlock solutions

    Rate each goal 1–4, do the blank-page recall, then try the 30-mark paper before opening the model answers.

What’s inside every lesson

↻ Spaced Do Now4 warm-up cards from earlier lessons
3D Story SceneRidge Road, Mallam Sule’s shed and the school lab, with the whole cast
Wonder Wall & Sort GamePin a prediction, then drag examples into the right bins
Virtual PracticalReadings from a physics model, with a live graph underneath
Concept ZoomForces, shadows, energy and resonance up close
Worked ExamplesEvery step written out with a note under each line
The BridgeEach lesson hands Zainab one more clue for the case
Quiz & 30-Mark Paper12 questions, self-rating 1–4, solutions unlock after you try
Nigerian NarratorA spoken, spotlighted tour in Nigerian English
Ready when you are

Let’s save Hajia Ramatu’s eggs.

Start with Lesson 1: count the okada’s bounces and put a number on its rhythm.

Start Lesson 1: Things That Repeat →