What determines the period of a spring oscillator?

The period is T = 2 pi sqrt(m/k) where m is mass and k is spring stiffness. Unlike a pendulum the period does not depend on amplitude. This simulator lets you verify this by changing the start position.

What is critical damping?

Critical damping occurs when b = 2 sqrt(km). The system returns to equilibrium as fast as possible without oscillating. Try the Overdamped preset to see this behavior compared to underdamped oscillations.

Spring Oscillator Simulator — Interactive Physics Lab

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Spring Oscillator