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Oscillations

Displacement, velocity and acceleration graphs

  • 2 things to know
  • Papers 2 and 3

Overview

Recall questions on the shapes of the three graphs, what each gradient gives, where velocity and acceleration are zero, and the phase difference between them.

What you need to know

Answer each one before you reveal it.

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Numbers

What does a displacement-time graph look like for an oscillator released from maximum displacement, what does its gradient give, and where is that gradient zero?

Numbers

What does a velocity-time graph look like for an oscillator, what does its gradient give, and where is the acceleration zero?

Questions from this subtopic

Each one with the model answer underneath.

  1. 1

    What does the displacement–time graph of an object released from maximum displacement and oscillating freely look like?

    Model answer

    It is a cosine curve starting at the peak, with a constant amplitude and a constant period.

  2. 2

    What does the gradient of a displacement–time graph give?

    Model answer

    It gives the velocity of the oscillator at that instant.

  3. 3

    Where on a displacement–time graph is the gradient zero, and what is the oscillator doing there?

    Model answer

    At the peaks and troughs, where the oscillator is momentarily at rest at maximum displacement before reversing.

  4. 4

    Where is the displacement–time graph steepest, and what does this tell you?

    Model answer

    It is steepest where it crosses the time axis, at the equilibrium position, showing that the oscillator is moving at its maximum speed there.

  5. 5

    What does the velocity–time graph look like for an oscillator whose displacement follows a cosine curve?

    Model answer

    It is a negative sine curve of the same period, with peak values of ±Aω.

  6. 6

    What does the gradient of a velocity–time graph give?

    Model answer

    It gives the acceleration of the oscillator at that instant.

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