Mass on a spring
A spring pulls with force F = -kx. The period depends on mass and stiffness, T = 2 pi sqrt(m/k), not on amplitude.
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Analogy
A stiffer spring bounces faster, a heavier mass bounces slower.
Example
T = 2 pi sqrt(m / k)T = 2 pi sqrt(0.5 / 200)T = 0.314 s
In practice
A 0.5 kg mass on a 200 N/m spring takes about 0.31 s per cycle.
Practice
Flashcards
- What does the period of a mass on a spring depend on?The mass and the spring constant, not the amplitude.
Questions people ask
Does gravity change the period of a vertical spring?
No. Gravity only shifts the equilibrium point lower, because the spring stretches until force balances weight. The oscillation about that new point still has period 2 pi sqrt(m/k). That is why the same spring has the same period on the Moon.
What is the spring constant?
The spring constant k measures stiffness in newtons per metre. A spring with k = 200 N/m needs 200 N to stretch it by 1 m. Hooke's law says force equals k times the stretch, as long as the spring is not stretched beyond its elastic limit.