Me

The mass on a spring and the pendulum Edexcel International A Level Physics revision

Not started

Learn it

In plain words

Two oscillators turn up again and again: a mass bouncing on a spring, and a pendulum. Each has a simple formula for how long one oscillation takes, and each has a surprise. The spring's timing doesn't care about gravity, and the pendulum's doesn't care about the mass.

4 things to know

  1. A mass m on a spring of stiffness k: T = 2π√(m ÷ k). A heavier mass is slower; a stiffer spring is faster.
  2. A simple pendulum of length l, for small swings: T = 2π√(l ÷ g). A longer pendulum is slower. The mass of the bob makes no difference.
  3. Both move in simple harmonic motion because the restoring force is proportional to the displacement: F = −kx.
  4. To measure a period well, time many oscillations and divide, and time from a marker at the centre of the motion, where the object is moving fastest.

Worked example

A 0.50 kg mass hangs from a spring of stiffness 200 N/m. Find the period of its oscillations.

  1. T = 2π√(m ÷ k) = 2π√(0.50 ÷ 200).
  2. = 2π × 0.050.
  3. = 0.31 s.

Tips and tricks

  • For a spring, T² is proportional to m. For a pendulum, T² is proportional to l. Plot T² to get a straight line.
  • The pendulum formula only works for small swings, up to about 10°.
5 questions, about 2 minutes.

It lands in your notebook with its questions as flashcards.

The mass on a spring and the pendulum: 5 questions and answers

These are the quiz’s questions. Do the quiz first, then come back here for the ones that got you.

  1. What does the period of a simple pendulum depend on?
    • its length (the answer)
    • the mass of the bob
    • the amplitude of a small swing
    • the material of the bob

    T = 2π√(l ÷ g).

  2. The mass on a spring is made four times bigger. What happens to the period?
    • It doubles. (the answer)
    • It becomes four times bigger.
    • It halves.
    • It stays the same.

    The period is proportional to √m.

  3. A pendulum is taken to the Moon, where g is smaller. What happens to its period?
    • It increases. (the answer)
    • It decreases.
    • It stays the same.
    • It becomes zero.

    A smaller g gives a larger T.

  4. A spring is swapped for a stiffer one, with the same mass. What happens to the period?
    • It decreases. (the answer)
    • It increases.
    • It stays the same.
    • It doubles.

    A bigger k gives a smaller T.

  5. Where is the best place for the marker used to time oscillations?
    • at the centre of the motion (the answer)
    • at one end of the motion
    • anywhere
    • above the support

    The object passes the centre fastest, so the moment it passes is easiest to judge.

Things you can type

Or go straight to

Or browse a shelf