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Creating Models

Solutions and graphs of simple harmonic motion

  • 2 things to know
  • Components 01, 02 and 03

Overview

Recall questions on the sine and cosine solutions of simple harmonic motion and when each applies, writing them with frequency, the displacement–time graph, the phase of velocity and acceleration against displacement, gradients linking the graphs, greatest speed at equilibrium, amplitude, angular frequency and maximum speed from x = 0.020 sin(30t), and spotting traces that are not simple harmonic.

What you need to know

Answer each one before you reveal it.

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Key term

What are the two standard solutions of the simple harmonic equation?

Key term

Which solution describes an oscillator released from maximum displacement at t = 0?

Questions from this subtopic

Each one with the model answer underneath.

  1. 1

    What are the two standard solutions of the simple harmonic equation?

    Model answer

    The displacement is x = A sin(ωt) or x = A cos(ωt), depending on where the timing starts.

  2. 2

    Which solution describes an oscillator released from maximum displacement at t = 0?

    Model answer

    The cosine solution x = A cos(ωt), because it gives x = A when t = 0.

  3. 3

    Which solution describes an oscillator passing through equilibrium at t = 0?

    Model answer

    The sine solution x = A sin(ωt), because it gives x = 0 when t = 0.

  4. 4

    Write the displacement equation in terms of frequency rather than angular frequency.

    Model answer

    The displacement is x = A sin(2πft) or x = A cos(2πft).

  5. 5

    Describe the shape of the displacement–time graph of a simple harmonic oscillator.

    Model answer

    It is a sinusoidal curve of constant amplitude and constant period about the equilibrium position.

  6. 6

    What is the phase relationship between displacement and velocity in simple harmonic motion?

    Model answer

    The velocity leads the displacement by a quarter of a cycle, that is by π/2 rad.

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