Angular frequency - Oscillations Video Lecture - Class 11

hello friends this video on oscillations
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going ahead with part 8 now let us talk
about the third term that is the angular
frequency in the expression that is
which is denoted by Omega so what is the
angular frequency it is nothing but the
frequency with which the mass M is
oscillating so how you can get an
expression for Omega now let us try to
find an expression for Omega so how can
we express Omega in terms of the other
terminologies which we studied till now
again we will start with the same
expression that is the displacement of
the particle which is denoted by a cos
Omega T plus Phi
let us say that the initial phase or the
initial state of the particle is it
starts from 0 so we are considering that
Phi is equal to 0 so in that case X of T
may be equal to a cos Omega T now as we
know that it is a cosine function so it
will repeat itself after 2 pi and
similarly since it is a simple harmonic
motion so after the time period of
capital T this explai this X of T will
also get repeat it so you can say that X
of T may be equal to H of T plus capital
T it is after this much of time period
the motion will get repeated right so we
can say that a cos Omega T
is equal to a cos Omega T plus capital T
which can be written as a cos Omega T
plus Omega capital T now we also know
that cos T that means itself after 2 pi
now from this expression we get also
mega T is equal to cos Omega T plus
Omega capital T but since we know that
cos of theta is equal to cos he done
thus 2 pi so comparing with this
equation we can say that this term Omega
T is nothing but 2 mic so we can say
Omega capital T is equal to 2 mu PI or
from here we can say that Omega is equal
to 2 pi by T so we can say that angular
frequency is related to the time period
of the oscillatory motion so that is
Omega is equal to 2 pi by T this is how
we define the angular frequency of an
oscillating particle so the SI unit of
angular frequency is radians per second
that is very obvious because angular
frequency is 2 pi by T so this Phi is
measured in radians and time is measured
in seconds so the SI unit becomes Radian
per second also
it is two pi times the frequency of
oscillation what is frequency of
oscillation we spoke about it in the
previous Lex frequency of oscillation is
nothing but the inverse of time period
that is the number of oscillations per
second by up by an oscillating body so
nu is equal to 1 by T this is the
frequency of oscillation so just now we
found that Omega is equal to 2 pi by T
so this can be written as 2 pi into 9 by
T which is equal to 2 pi interview so it
is 2 pi times the frequency of
oscillation thank you please visit exam
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