Some Important Definitions

**Category : **JEE Main & Advanced

**(1) Time period (T) :** It is the least interval of time after which the periodic motion of a body repeats itself. S.I. unit of time period is second.

**(2) Frequency (n) :** It is defined as the number of oscillations executed by body per second. S.I unit of frequency is hertz (Hz).

**(3) Angular Frequency \[(\omega )\]:** Angular frequency of a body executing periodic motion is equal to product of frequency of the body with factor \[2\pi \]. Angular frequency \[\omega =2\pi n\] Its unit is rad/sec.

**(4) Phase \[(\phi )\]:** Phase of a vibrating particle at any instant is a physical quantity, which completely express 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 generalised equation of motion of the vibrating particle.

\[y=a\sin \theta =a\sin (\omega \,t+{{\varphi }_{0}})\]

here, \[\theta =\omega \,t+{{\varphi }_{0}}\]= phase of vibrating particle.

\[{{\phi }_{0}}=\]Initial phase or epoch. It is the phase of a vibrating particle at \[t=0\].

**(1) Same phase :** Two vibrating particle are said to be in same phase, if the phase difference between them is an even multiple of \[\pi \] or path difference is an even multiple of \[(\lambda /2)\] or time interval is an even multiple of (T / 2) because 1 time period is equivalent to \[2\pi \] rad or 1 wave length \[(\lambda )\].

**(2) 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 \[{{180}^{o}}\].

Opposite phase means the phase difference between the particle is an odd multiple of \[\pi (say\,\,\pi ,\,\,3\pi ,\,\,5\pi ,\,\,7\pi .....)\] or the path difference is an odd multiple of \[\lambda (\text{say}\,\,\frac{\lambda }{2},\,\frac{3\lambda }{2}\,,......)\] or the time interval is an odd multiple of (T / 2).

**(3) Phase difference : **If two particles performs S.H.M and their equation are

\[{{y}_{1}}=a\sin (\omega \,t+{{\varphi }_{1}})\]and \[{{y}_{2}}=a\sin (\omega \,t+{{\varphi }_{2}})\] then phase difference \[\Delta \varphi =(\omega \,t+{{\varphi }_{2}})-(\omega \,t+{{\varphi }_{1}})\]\[={{\varphi }_{2}}-{{\varphi }_{1}}\]

*play_arrow*Periodic and Oscillatory (Vibratory) Motion*play_arrow*Simple Harmonic Motion*play_arrow*Some Important Definitions*play_arrow*Displacement in S.H.M.*play_arrow*Velocity in S.H.M.*play_arrow*Acceleration in S.H.M.*play_arrow*Comparative Study of Displacement Velocity and Acceleration*play_arrow*Energy in S.H.M.*play_arrow*Average Value of P.E. and K.E.*play_arrow*Differential Equation of S.H.M.*play_arrow*How to Find Frequency and Time Period of S.H.M.*play_arrow*Simple Pendulum*play_arrow*Factor Affecting Time Period of Simple Pendulum*play_arrow*Oscillation of Pendulum in Different Situations*play_arrow*Some Other Types of Pendulum*play_arrow*Spring System*play_arrow*Spring Pendulum*play_arrow*Oscillation of Spring Combination*play_arrow*Various Formulae of S.H.M.*play_arrow*Free, Damped, Forced and Maintained Oscillations*play_arrow*Super Position of S.H.M's (Lissajous Figures)

You need to login to perform this action.

You will be redirected in
3 sec