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Simple Harmonic Motion

Defining simple harmonic motion and a = −ω²x

  • 3 things to know
  • Unit A2 1

Overview

Simple harmonic motion, significance of the minus sign in a = −ω²x and equation relating angular frequency to frequency and define every symbol.

What you need to know

Answer each one before you reveal it.

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Numbers

A body oscillates with simple harmonic motion of amplitude 0.050 m at a frequency of 2.0 Hz. Calculate its maximum acceleration.

Key term

State the defining equation of simple harmonic motion and define every symbol.

Key term

What is the significance of the minus sign in a = −ω²x?

Questions from this subtopic

Each one with the model answer underneath.

  1. 1

    Define simple harmonic motion.

    Model answer

    Simple harmonic motion is motion in which the acceleration of a body is directly proportional to its displacement from a fixed equilibrium position and is always directed towards that position.

  2. 2

    State the defining equation of simple harmonic motion and define every symbol.

    Model answer

    a = −ω²x, where a is the acceleration in m s⁻², ω the angular frequency in rad s⁻¹ and x the displacement from the equilibrium position in metres.

  3. 3

    What is the significance of the minus sign in a = −ω²x?

    Model answer

    The minus sign shows that the acceleration is always in the opposite direction to the displacement, so the body is always accelerated back towards the equilibrium position.

  4. 4

    State the equation relating angular frequency to frequency and define every symbol.

    Model answer

    ω = 2πf, where ω is the angular frequency in rad s⁻¹ and f the frequency of the oscillation in hertz.

  5. 5

    How is the angular frequency of an oscillation related to its period?

    Model answer

    ω = 2π/T, where T is the period of the oscillation in seconds, so the angular frequency is the number of radians of phase completed each second.

  6. 6

    Define the amplitude of an oscillation.

    Model answer

    The amplitude is the maximum displacement of the oscillating body from its equilibrium position, measured in metres.

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