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Period of a mass–spring system and a simple pendulum

  • 2 things to know
  • Components 01, 02 and 03

Overview

Recall questions on the two period equations and frequency, calculations for given masses, stiffnesses and lengths, why the bob's mass does not matter, timing from equilibrium, and squared-period graphs.

What you need to know

Answer each one before you reveal it.

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Key term

What equation gives the period of a mass oscillating on a spring?

Key term

What equation gives the period of a simple pendulum?

Questions from this subtopic

Each one with the model answer underneath.

  1. 1

    What equation gives the period of a mass oscillating on a spring?

    Model answer

    The period is T = 2π√(m/k).

  2. 2

    What equation gives the period of a simple pendulum?

    Model answer

    The period is T = 2π√(L/g), where L is the length to the centre of the bob.

  3. 3

    How are period and frequency related?

    Model answer

    The frequency is the reciprocal of the period, f = 1/T.

  4. 4

    A 0.20 kg mass oscillates on a spring of stiffness 20 N m⁻¹. What is the period?

    Model answer

    T = 2π√(0.20/20) = 2π × 0.10 = 0.63 s.

  5. 5

    A 0.50 kg mass hangs on a spring of stiffness 32 N m⁻¹. What is the frequency of oscillation?

    Model answer

    T = 2π√(0.50/32) = 0.79 s, so f = 1/T = 1.3 Hz.

  6. 6

    Calculate the period of a simple pendulum of length 0.25 m.

    Model answer

    T = 2π√(0.25/9.81) = 1.0 s.

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