KinexiaLEARN PHYSICS

Spring Period — Trampoline Bounce (Worked Example)

Medium
Problem

A trampoline's effective spring constant is 5000 N/m. A 50 kg jumper bounces on it. What is the period of small bounces?

Given

  • m = 50 kg

  • k = 5000 N/m

Find

The period T.

Principle

Small bounces are approximately simple harmonic: T = 2π√(m/k).

Formula

Solution

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

  2. Substitute: T=2π50/5000T = 2\pi\sqrt{50/5000}

  3. Inside: 50/5000=0.0150/5000 = 0.01; 0.01=0.10\sqrt{0.01} = 0.10

  4. Multiply: T=2π×0.10=0.628 sT = 2\pi \times 0.10 = 0.628\ \mathrm{s}

0.628 s

Unit check

√(kg ÷ kg/s²) = s — correct.

What this means physically

0.628 s — about 1.6 bounces per second for small hops. Big jumps leave the mat (free flight), so this only describes gentle bouncing where contact is maintained.

Common mistake

Applying the formula to huge jumps. T = 2π√(m/k) assumes the mass stays on the spring — airborne time follows projectile motion instead.