Simple Harmonic Motion Period (Spring)

📊 beginner

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

Period of oscillation for a mass on a spring.

Variables & Units

$T$

Period

Unit: $\text{s}$

$m$

Mass

Unit: $\text{kg}$

$k$

Spring constant

Unit: $\text{N/m}$

Key Information

📐 Derived From

Hooke's law $F=-kx$ and Newton's second law

💡 Example

Mass $0.5\,\text{kg}$ on spring with $k=200\,\text{N/m}$: $T = 2\pi\sqrt{0.5/200} = 2\pi\sqrt{0.0025} = 2\pi \times 0.05 \approx 0.314\,\text{s}$.

🔧 Applications

Suspension systems, seismometers, clock pendulums

⚠️ Constraints

Ideal spring, no damping, small oscillations

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