Topic · 10 games

Oscillations: simple harmonic motion and resonance

A pendulum or a mass on a spring swings back and forth with its own steady rhythm, whatever the size of the swing. Energy flows between motion and storage, and pushes in time with the rhythm build a big motion: T = 2π·√(L ÷ g), T = 2π·√(m ÷ k), E = ½·k·A².

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10 games

PLAY NOW · 55

Metronome Studio: Keep the Beat

The period is the time for one beat; the frequency is how many beats fit in a second. Turn tempos into periods and hertz into beats per minute, count beats, and find when two metronomes click together.

PeriodFrequency
Play Metronome Studio
Frequency
f = 1 ÷ T
Tempo
tempo = 60·f

PLAY NOW · 56

Harbour Buoy: How Big Is the Swing?

Amplitude is how far an oscillation swings from the middle, not from top to bottom. Read it off a harbour post, see the period stay the same on a bigger swell, and find distances, speeds, and energies.

AmplitudeSimple harmonic motion
Play Harbour Buoy
Amplitude
A = (y_max − y_min) ÷ 2
Top speed
v_max = 2π·A ÷ T

PLAY NOW · 57

Seismograph: Read the Shaking

A seismograph turns shaking into a wavy line. Read the period from the peak spacing and the paper speed, the frequency from the period, and the ground's tiny amplitude from the magnified trace.

Period and frequencyAmplitude
Play Seismograph
Period
T = d ÷ u
Amplitude
x = a ÷ M

PLAY NOW · 58

Pendulum Clock: Keep the Beat

A pendulum's period depends only on its length and on g: T = 2π·√(L ÷ g). Build a seconds pendulum, time a short one, double a period, swing one on the Moon, and try a heavier bob.

Simple harmonic motionPendulum
Play Pendulum Clock
Period
T = 2π·√(L ÷ g)
Seconds pendulum
L = g·(T ÷ 2π)²

PLAY NOW · 59

Wrecking Ball: Height Becomes Speed

A swinging ball trades height for speed and back: v = √(2·g·h). Find speeds at the bottom and partway down, the rope's pull, Galileo's peg, and the angle a given speed reaches.

PendulumEnergy conservation
Play Wrecking Ball
Drop
h = L·(1 − cos θ)
Speed
v = √(2·g·h)

PLAY NOW · 61

Spring Bounce: Stretch, Bounce, Repeat

A spring pulls back with k·x, and a mass on it bounces with T = 2π·√(m ÷ k). Find a stretch, a period, a spring, a top speed, and a period from the stretch alone.

Simple harmonic motionHooke's law
Play Spring Bounce
Hooke's law
F = k·x
Period
T = 2π·√(m ÷ k)

PLAY NOW · 62

Spring Shop: Side by Side or End to End?

Springs side by side share the load and act stiffer; end to end, each carries it all and they act softer. Predict stretches, the stiffness of half a spring and of a mixed pair, and a bounce.

Hooke's lawSprings combined
Play Spring Shop
Side by side
k = k₁ + k₂
End to end
1/k = 1/k₁ + 1/k₂

PLAY NOW · 63

Spring Launcher: Push, Store, Release

A squashed spring stores ½·k·x² and hands it on when let go. Launch a pinball and a rocket, aim for a platform, see what doubling the push does, and stop a cart with a spring.

Elastic energyEnergy conservation
Play Spring Launcher
Stored energy
E = ½·k·x²
Launch
v = x·√(k ÷ m)

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