KinexiaLEARN PHYSICS

Spring Period — Car Suspension Bounce (Worked Example)

Medium
Problem

A car's suspension has spring constant 30,000 N/m per wheel, and each wheel supports 400 kg. What is the period of the car's vertical bounce?

Given

  • m = 400 kg

  • k = 30,000 N/m

Find

The period T.

Principle

A mass on a spring oscillates with T = 2π√(m/k). Car designers tune this near 1 Hz for comfort.

Formula

Solution

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

  2. Substitute: T=2π400/30000T = 2\pi\sqrt{400/30000}

  3. Inside: 400/30000=0.01333400/30000 = 0.01333; 0.01333=0.1155\sqrt{0.01333} = 0.1155

  4. Multiply: T=2π×0.1155=0.726 sT = 2\pi \times 0.1155 = 0.726\ \mathrm{s}

0.726 s

Unit check

√(kg ÷ N/m) = √(kg ÷ kg/s²) = s — correct.

What this means physically

0.726 s per bounce (≈1.38 Hz) — the familiar gentle bobbing after a speed bump. Stiffer springs or lighter cars would bounce faster and feel harsher.

Common mistake

Using the whole car's mass. The formula needs the mass per spring — divide by 4 wheels first.