# JEE Main & Advanced Physics Simple Harmonic Motion Some Important Definitions

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}}$

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