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Vibrations

The simple pendulum

  • 3 things to know
  • Component 1

Overview

Recall questions on T = 2π√(l/g), why the period does not depend on the mass of the bob, the small-angle condition, worked period and length calculations, and using a pendulum to determine the acceleration of free fall.

What you need to know

Answer each one before you reveal it.

Your recallNot started
Key term

State the equation for the period of a simple pendulum, defining every symbol and its unit.

Key term

Explain why a simple pendulum is only approximately a simple harmonic oscillator.

Key term

Under what condition does a simple pendulum perform simple harmonic motion?

Questions from this subtopic

Each one with the model answer underneath.

  1. 1

    State the equation for the period of a simple pendulum, defining every symbol and its unit.

    Model answer

    The equation is T = 2π√(l/g), where T is the period in s, l is the length of the pendulum in m and g is the gravitational field strength in N kg⁻¹.

  2. 2

    What is a simple pendulum?

    Model answer

    A simple pendulum is a small heavy bob suspended from a fixed point by a light inextensible string, free to swing in a vertical plane.

  3. 3

    Under what condition does a simple pendulum perform simple harmonic motion?

    Model answer

    The angular amplitude must be small, typically less than about 10°, so that the restoring force is very nearly proportional to the displacement.

  4. 4

    Which force provides the restoring force for a simple pendulum?

    Model answer

    The component of the bob's weight along the arc, mg sin θ, acts back towards the lowest point and provides the restoring force.

  5. 5

    Explain why a simple pendulum is only approximately a simple harmonic oscillator.

    Model answer

    The restoring force is proportional to sin θ rather than to θ itself, and the two agree only for small angles, so the motion departs from simple harmonic at large amplitudes.

  6. 6

    How is the length of a simple pendulum measured for use in T = 2π√(l/g)?

    Model answer

    The length is measured from the point of support to the centre of the bob, so the radius of the bob is added to the length of the string.

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