KinexiaLEARN PHYSICS

Spring Period — Diving Board (Worked Example)

Medium
Problem

A diving board behaves like a spring with k = 4000 N/m. A 70 kg diver bounces on its end. What is the period of the bounce?

Given

  • m = 70 kg

  • k = 4000 N/m

Find

The period T.

Principle

The board-diver system is a mass-spring oscillator: T = 2π√(m/k). Divers time their jump to this rhythm.

Formula

Solution

  1. Write the formula: T=2πm/kT = 2\pi\sqrt{m/k}

  2. Substitute: T=2π70/4000T = 2\pi\sqrt{70/4000}

  3. Inside: 70/4000=0.017570/4000 = 0.0175; 0.0175=0.1323\sqrt{0.0175} = 0.1323

  4. Multiply: T=2π×0.1323=0.831 sT = 2\pi \times 0.1323 = 0.831\ \mathrm{s}

0.831 s

Unit check

√(kg ÷ kg/s²) = s — correct.

What this means physically

0.831 s — the diver bounces about 1.2 times per second and launches at the top of a bounce, converting the board's stored energy into height.

Common mistake

Using the diver's weight (686 N) as m. The formula needs mass in kg — divide weight by g first.