Simple harmonic motion

Oscillations repeat because a restoring force pulls the system back toward equilibrium. The most important quantities are period, frequency, amplitude, and angular frequency.

Core formulas

Spring period

T = 2 pi sqrt(m / k)

Heavier mass means slower oscillation

Pendulum period

T = 2 pi sqrt(L / g)

Longer pendulum means slower oscillation

Frequency

f = 1 / T

Cycles per second

Angular frequency

omega = 2 pi f

The phase changes this fast

Energy in SHM

In ideal simple harmonic motion, total mechanical energy stays constant. The system keeps trading energy between kinetic and potential forms as it moves between equilibrium and the turning points.

Interactive lab

Simple Harmonic Motion

Mass: 1 kg

Spring Constant: 10 N/m

Amplitude: 0.5 m

Period

1.987 s

Frequency

0.503 Hz

omega (rad/s)

3.162

Max speed (m/s)

1.581

Spring-Mass Period

T = 2 pi sqrt(m / k) = 2 pi sqrt(1 / 10) = 1.987 s

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Quick reference

Amplitude: Maximum displacement
Period: Time for one cycle