Simple Harmonic Motion as a Second-Order Equation · seed 1 · A4, ink-friendly. The answer key prints on its own page for grown-ups.

The swing that keeps its tempo

Science · Forces & Motion · ages 18-20
Name ______________________   Date ____________

  1. The period and frequency of a simple harmonic oscillator ignore amplitude.

    Circle one:   True   False

  2. What is the defining mark of simple harmonic motion?

    • Acceleration proportional to minus displacement
    • Velocity that never changes
    • A force that always points the same way

  3. What sets the natural frequency of a mass on a spring?

    • How far you pull it before release
    • Square root of k over m
    • The phase of the cosine

  4. How do you fit amplitude and phase to a real trip?

    • Measure the spring constant twice
    • Use position at time zero plus velocity at time zero
    • Copy them from a different oscillator

  5. What sets the frequency of a small swing pendulum?

    • Square root of g over length
    • Square root of length over mass
    • The weight of the bob alone

  6. A heavy rider and a light rider take turns on the same diving board. Who bounces more slowly?

    • The light rider, since less mass means longer period
    • Both bounce at exactly the same rate
    • The heavy rider, since more mass means longer period

  7. Two pendulums share one length but carry different bobs. How do their tempos compare?

    • The heavier bob swings faster
    • The lighter bob swings faster
    • They swing at the same tempo

  8. A student swings a pendulum through 60 degrees and uses the small angle formula. What is wrong?

    • The formula needs small swings where sine matches the angle
    • Large swings always run faster than small ones
    • Pendulums never obey harmonic motion at all
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Answer key

For grown-ups. Fold this page away before handing over the rest.

The swing that keeps its tempo W1-mt_HHmR-uCvwO-s1

  1. True · Gentle or hard plucks of a guitar string give the same tone.
  2. Acceleration proportional to minus displacement · A restoring push toward rest, growing with displacement, makes the motion sinusoidal.
  3. Square root of k over m · Stiffer springs run faster and heavier masses run slower, through square root of k over m.
  4. Use position at time zero plus velocity at time zero · Two unknowns need two starting conditions, one for position and one for velocity.
  5. Square root of g over length · Short strings and strong gravity hurry the swing through square root of g over length.
  6. The heavy rider, since more mass means longer period · Period grows with mass, so the heavy rider oscillates more slowly.
  7. They swing at the same tempo · Tempo depends on g and length only, so bob mass drops out.
  8. The formula needs small swings where sine matches the angle · Past about 15 degrees the sine drifts from the angle, so the equation changes shape.
Worksheet · LightMySky