# Angular Frequency

Angular frequency of a body executing periodic motion is equal to product of frequency of the body with factor 2

*Ï€*.Angular frequency,

*Ï‰*= 2*Ï€**n*.The SI unit of

*Ï‰*is Hz (SI). It also represents angular velocity. In that case, the unit will be rad/s.# Displacement

In general, the name displacement is given to a physical quantity which undergoes a change with time in a periodic motion.

# Phase

Phase of a vibrating particle at any instant is a physical quantity, which completely expresses the position and direction of motion of the particle at that instant with respect to its mean position.

In oscillatory motion, the phase of a vibrating particle is the argument of sine or cosine function involved to represent the generalized equation of motion of the vibrating particle.

*y*=

*Î±*sin

*Î¸*=

*Î±*sin (

*Ï‰t*+

*Ï†*

_{0})

Here,

*Î¸*=*Ï‰t*+*Ï†*_{0}= phase of vibrating particle.# Initial phase or epoch

It is the phase of a vibrating particle at

*t*= 0.In

*Î¸*=*Ï‰t*+*Ï†*_{0}, when*t*= 0;*Î¸*=*Ï†*_{0}*t*= 0; here,*Ï†*_{0}is the angle of epoch.# Same phase

Two vibrating particles are said to be in same phase, if the phase difference between them is an even multiple of

*Ï€*or path difference is an even multiple of (*Î»*/2) or time interval is an even multiple of (*T*/2) because 1 time period is equivalent to 2*Ï€**rad or 1 wavelength (**Î»*).# Opposite phase

When the two vibrating particles cross their respective mean positions at the same time moving in opposite directions, then the phase difference between the two vibrating particles is 180Â°.

Opposite phase means the phase difference between the particle is an odd multiple of

*Ï€*(say*Ï€*, 3*Ï€*, 5*Ï€*, 7*Ï€*,...) or the path difference is an odd multiple of*Î»*or the time interval is an odd multiple of (*T*/2).# Phase difference

If two particles perform simple harmonic motion and their equation are

*y*

_{1}=

*Î±*sin (

*Ï‰t*+

*Ï†*

_{1}) and

*y*

_{2}=

*Î±*sin (

*Ï‰t*+

*Ï†*

_{2})

then phase difference

Î”

*Ï†*= (*Ï‰t*+*Ï†*_{2}) â€“ (*Ï‰t*+*Ï†*_{1}) =*Ï†*_{2}â€“*Ï†*_{1}