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Oscillations

The conditions for simple harmonic motion

  • 2 things to know
  • Papers 2 and 3

Overview

Recall questions on the definition, the condition on the restoring force, what the minus sign means, the acceleration-displacement relationship, and an oscillation that is not simple harmonic.

What you need to know

Answer each one before you reveal it.

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Numbers

What is the relationship between acceleration and displacement in simple harmonic motion, and what is an example of an oscillation that is not simple harmonic?

Numbers

What do the period and the frequency of an oscillation mean, and what is angular frequency and its unit?

Questions from this subtopic

Each one with the model answer underneath.

  1. 1

    What is meant by simple harmonic motion?

    Model answer

    It is motion in which the acceleration is proportional to the displacement from the equilibrium position and is always directed back towards that position.

  2. 2

    State the condition on the restoring force for simple harmonic motion:

    Model answer

    The restoring force must obey F = −kx, so it is proportional to displacement and acts in the opposite direction.

  3. 3

    What is the significance of the minus sign in F = −kx?

    Model answer

    It shows the force always acts back towards the equilibrium position, opposite to the displacement.

  4. 4

    Why does a mass hanging on a spring perform simple harmonic motion when it is displaced vertically?

    Model answer

    An extra displacement x stretches the spring further, producing an extra force kx directed back towards equilibrium, which is exactly the condition F = −kx.

  5. 5

    What is an example of an oscillation that is not simple harmonic, and why is it not?

    Model answer

    A ball bouncing on the ground is not simple harmonic, because the force on it is not proportional to its displacement from any equilibrium position.

  6. 6

    State the relationship between acceleration and displacement for a simple harmonic oscillator:

    Model answer

    a = −ω²x, where ω is the angular frequency.

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