Physics Hooke's Law

Spring Force & Potential Energy

Apply Hooke's Law (F = −kx) and compute elastic potential energy (PE = ½kx²). Optionally find the period of oscillation when mass is given.

F = −kx (Hooke's Law)

PE = ½kx²

T = 2π√(m/k)

Live

Inputs

Mode

Spring Constant k (N/m)

Stiffness of the spring — always positive.

Displacement x (m)

Positive = stretched, negative = compressed.

Applied Force F (N)

The restoring force magnitude.

Mass m (kg) — optional

If provided, calculates oscillation period T and frequency f.

Results

Restoring Force F

—

F = −kx (directed back toward equilibrium)

—

PE (J)

—

Displacement (m)

—

Period T (s)

—

Frequency f (Hz)

Step-by-Step Solution

Spring Visualization

Hooke's Law

F = −kx

The restoring force F is proportional to displacement x and always opposes it. k is the spring constant (N/m), x is displacement from equilibrium (m).

Elastic Potential Energy

PE = ½kx²

Energy stored in a stretched or compressed spring. Always non-negative. When mass is given: T = 2π√(m/k), f = 1/T, ω = 2πf.

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