How to play Spring Bounce
- Choose a test and read the mass, the spring, the pull, or the stretch on the card.
- Hooke's law: a spring pulls back with k·x. At rest it holds up the weight, k·x₀ = m·g.
- Pulled and let go, the mass bounces with T = 2π·√(m ÷ k) and a top speed A·√(k ÷ m). Type your prediction and press Start.
- Watch the graph: the position draws a sine curve, and the period is the time from one peak to the next.
Why does a mass on a spring bounce so evenly?
A spring pulls back in proportion to how far it is stretched or squeezed: F = k·x, Hooke's law. Hang a mass on it and it stretches until the spring's pull matches the weight, at x₀ = m·g ÷ k. Pull it further and let go, and the extra pull is always proportional to the distance from that rest position, pointing back towards it. That is what makes simple harmonic motion: the mass rises and falls in a perfect sine curve, y = A·cos(ω·t), with ω = √(k ÷ m) and a period T = 2π·√(m ÷ k). A heavier mass bounces more slowly, a stiffer spring faster, and the size of the pull makes no difference to the period: a bigger bounce simply moves faster. The mass is fastest through the middle, at A·ω, and stops for an instant at each end. Since m ÷ k = x₀ ÷ g, you can even predict the period from how much the spring sags: T = 2π·√(x₀ ÷ g).
A focused learning model
The spring is light and obeys Hooke's law perfectly, and there is no friction, so nothing slows the bounce. To find the stretch, the mass is lowered gently over 2 s to rest. For a bounce, the mass is pulled 5 cm below its rest position and let go, and the run lasts 2 s. When the stiffness is asked, the mass bounces on your spring and the graph marks the period wanted. Lengths are to scale. Answers within 2% are right. g = 9.8 m/s². Plays in real time.