Phase and phase constant

Intermediate

Starting point of the oscillation cycle.

The phase ωt + φ gives the stage in the cycle; φ tells where it starts. Two oscillations with the same ω but different φ are shifted in time.

Worked example

Starting at the centre moving up: φ = −π/2 in the cos form.

Common mistake

Phase is in radians.

In more detail

The phase of an oscillation is the argument of the sinusoid, ωt + φ. It describes where the system is in its cycle at a given time.

Phase is used in radio communication to encode information.
Noise-cancelling headphones rely on controlling the phase of sound waves.
Two pendulums started at different moments have different phase constants, even though their periods are the same.

What is the phase constant?

The value of the phase at time zero, which sets the starting point of the cycle.

Is phase measured in radians?

Yes, usually in radians, though degrees are also used.

How is the phase constant found?

From the initial displacement and velocity, using the starting point of the cycle at time zero.