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Vibrations

Oscillating systems and energy

  • 3 things to know
  • A2 Unit 3

Overview

Recall questions on Oscillating systems and energy.

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Answer each one before you reveal it.

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Key term

State the equation for the period of a mass on a spring.

Key term

How does the period of a mass–spring system change if the mass is quadrupled?

Numbers

Calculate the period of a 0.25 kg mass on a spring of stiffness 40 N m⁻¹.

Questions from this subtopic

Each one with the model answer underneath.

  1. 1

    State the equation for the period of a mass on a spring.

    Model answer

    T = 2π√(m/k), where m is the mass and k is the stiffness, the force per unit extension.

  2. 2

    How does the period of a mass–spring system change if the mass is quadrupled?

    Model answer

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

  3. 3

    Calculate the period of a 0.25 kg mass on a spring of stiffness 40 N m⁻¹.

    Model answer

    T = 2π√(0.25 ÷ 40) = 2π × 0.079 = 0.50 s.

  4. 4

    State the equation for the period of a simple pendulum.

    Model answer

    T = 2π√(l/g), where l is the length of the pendulum and g is the gravitational field strength.

  5. 5

    Why does the period of a simple pendulum not depend on the mass of the bob?

    Model answer

    The restoring force is proportional to the mass, and so is the inertia, so the mass cancels in the equation of motion.

  6. 6

    Calculate the length of a simple pendulum whose period is 2.0 s, taking g as 9.81 m s⁻².

    Model answer

    Rearranging gives l = gT² ÷ 4π² = 9.81 × 4.0 ÷ 39.5 = 0.99 m.

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