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Further Mechanics and Thermal Physics

Simple harmonic motion (SHM)

  • 6 things to know
  • Papers 2 and 3

Overview

The defining condition a = −ω²x, the displacement, velocity and acceleration equations, and the graphs.

What you need to know

Answer each one before you reveal it.

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Numbers

How is simple harmonic motion defined, and which way does the acceleration point?

Numbers

What do the symbols in a = −ω²x mean, and why is a cosine used for displacement?

Numbers

How is velocity expressed in SHM, and why does the equation carry a ± sign?

Numbers

Where is speed greatest in SHM, and how does the velocity graph relate to displacement?

Numbers

At maximum displacement in SHM, what are the velocity and acceleration?

Numbers

What happens as an oscillator passes through the centre, and what shape is the displacement graph?

Questions from this subtopic

Each one with the model answer underneath.

  1. 1

    In the definition of simple harmonic motion, what is the relationship between acceleration and displacement?

    Model answer

    Acceleration is directly proportional to displacement from the equilibrium position.

  2. 2

    In which direction is the acceleration always directed in simple harmonic motion?

    Model answer

    The acceleration is always directed towards the equilibrium position.

  3. 3

    State the defining equation for simple harmonic motion that relates acceleration to angular frequency and displacement.

    Model answer

    a = −ω²x

  4. 4

    In the equation a = −ω²x, what do each of the symbols represent?

    Model answer

    a is acceleration, ω is angular frequency, and x is displacement from equilibrium.

  5. 5

    State the equation that describes how displacement varies with time for an object undergoing SHM starting at maximum displacement.

    Model answer

    x = A cos(ωt)

  6. 6

    Why is a cosine function used rather than a sine function when describing displacement in SHM starting from maximum displacement?

    Model answer

    The cosine function has its maximum value at t = 0, which corresponds to the object starting at maximum displacement.

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