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ScientistGrades 11–12⏱ 20 min

Springs and pendulums

Set a spring or pendulum swinging, watch it draw a sine wave, and find what sets its rhythm.

Standards: HS-PS3-1HS-PS3-2

1Wonder

A grandfather clock keeps time with a swinging pendulum. A car’s springs bounce after a bump. Why do they both swing with such a steady rhythm, and what controls how fast?

2Explore

Oscillation lab

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Turn your phone sideways, or open this lesson on a tablet or computer. The explanation and quiz below work here.

0.5 kgF■ Motion energyStored energy ■123456time (s)xSillyChili
Measured period … Formula: T = 2π√(m/k) = 0.99 s
Oscillator
Try this
  • Drag the mass down and let go. What shape does the graph make?
  • Make the mass 4 times bigger. What happens to the period?
  • Pull it a little or a lot. Does the period change?
  • Switch to the pendulum. Try a small swing and then a big one (60°+). Compare the measured period with the formula.
  • Take the pendulum to the Moon. Does it swing faster or slower?
  • Turn on friction and watch the energy bar.

3Explain

F = −kxxSillyChili
Step 1 of 5

Pulled away, pulled back

Stretch a spring by x and it pulls back with a force F = −kx: the farther you pull, the harder it pulls back toward the middle. This is called a restoring force.

Periods

Spring: T=2πmkT = 2\pi\sqrt{\dfrac{m}{k}}

Pendulum (small swings): T=2πLgT = 2\pi\sqrt{\dfrac{L}{g}}

The pendulum formula only works for small swings. At 60° the real period is about 7% longer, which the simulation shows because it does not use the small-angle shortcut.

4Practice

Question 1 of 5

A spring has a period of 1 s. You make the mass 4 times bigger. What is the new period?

5Recap

  • A restoring force pulls back toward the middle: for a spring F=−kxF = -kx.
  • The motion is simple harmonic: position vs. time is a sine wave.
  • Spring: T=2πm/kT = 2\pi\sqrt{m/k}. Pendulum (small swings): T=2πL/gT = 2\pi\sqrt{L/g}.
  • The period does not depend on the amplitude (for a spring, and for small pendulum swings).
  • Energy swaps between stored and motion energy; friction slowly removes it.