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Oscillations

The mass-spring oscillator and the simple pendulum

  • 1 thing to know
  • Papers 2 and 3

Overview

Recall questions on both period equations and the assumption behind the pendulum's, why amplitude and bob mass do not matter, and determining g or a spring constant from oscillations.

What you need to know

Answer each one before you reveal it.

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Numbers

What is the phase relationship between displacement and velocity, what is the period of a mass-spring oscillator, and what happens if the mass is quadrupled?

Questions from this subtopic

Each one with the model answer underneath.

  1. 1

    State the equation for the period of a mass–spring oscillator:

    Model answer

    T = 2π√(m/k), where k is the spring constant.

  2. 2

    How does the period of a mass–spring oscillator depend on the amplitude?

    Model answer

    It does not depend on it at all, which is why such an oscillator keeps good time as its amplitude decays.

  3. 3

    The mass on a spring is increased fourfold. What happens to the period of oscillation?

    Model answer

    The period doubles, because T is proportional to the square root of the mass.

  4. 4

    A spring is replaced by a stiffer one of the same natural length. What happens to the period?

    Model answer

    The period decreases, because T is inversely proportional to the square root of the spring constant.

  5. 5

    State the equation for the period of a simple pendulum and the assumption it relies on:

    Model answer

    T = 2π√(l/g), valid provided the angular amplitude is small.

  6. 6

    Does the period of a simple pendulum depend on the mass of the bob?

    Model answer

    No, the mass cancels out, so the period depends only on the length of the pendulum and the local gravitational field strength.

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