Spring-Mass Period

Period of a Spring-Mass System

A mass $m$ on a spring with constant $k$ oscillates with angular frequency:

$\omega = \sqrt{\frac{k}{m}}$

The period (time for one complete oscillation):

$T = \frac{2\pi}{\omega} = 2\pi\sqrt{\frac{m}{k}}$

Units: seconds.

Hooke's Law

The spring force: $F = -kx$. The spring constant $k$ (N/m) measures stiffness — a stiffer spring (larger $k$) oscillates faster.

Key Observations

• Period increases with mass: heavier objects oscillate more slowly ($T \propto \sqrt{m}$)
• Period decreases with stiffness: stiffer springs oscillate faster ($T \propto 1/\sqrt{k}$)
• Period is independent of amplitude: whether you stretch the spring 1 cm or 10 cm, the period is the same (for ideal springs)

Examples

Your Task

Implement springPeriod(m, k) returning the oscillation period in seconds.