91Ó°ÊÓ

Angular frequency is defined as frequency of a periodic process.

It is given by

$\mathit{Ó\neg }\mathbf{=}\frac{\mathbf{2}\mathbf{Ï€}}{\mathbf{T}}$

Here,

$\mathit{T}$is the time period

Angular velocity is defined as the time rate at which an object rotates or revolves, about an axis.

For a simple pendulum it is given by

$\frac{\mathbf{∆}\mathbf{θ}}{\mathbf{∆}\mathbf{T}}\mathbf{=}\frac{{\mathbf{θ}}_{\mathbf{2}}\mathbf{-}{\mathbf{θ}}_{\mathbf{1}}}{{\mathbf{t}}_{\mathbf{2}}\mathbf{-}{\mathbf{t}}_{\mathbf{1}}}$

Angular Frequency is given by

$\mathit{Ó\neg }\mathbf{=}\frac{\mathbf{2}\mathbf{Ï€}}{\mathbf{T}}$

Here,

$\mathit{T}$is the time period

And, For a simple pendulum Angular velocity is given by

$\frac{\mathbf{∆}\mathbf{θ}}{\mathbf{∆}\mathbf{T}}\mathbf{=}\frac{{\mathbf{θ}}_{\mathbf{2}}\mathbf{-}{\mathbf{θ}}_{\mathbf{1}}}{{\mathbf{t}}_{\mathbf{2}}\mathbf{-}{\mathbf{t}}_{\mathbf{1}}}$

Also, we know that time period is given by

$\mathit{T}\mathbf{=}\mathbf{2}\mathit{Ï€}\sqrt{\frac{\mathbf{L}}{\mathbf{g}}}$

Here,

$\mathit{T}$is the time period

$\mathit{L}$is the length of the string to the pendulum

$\mathit{g}$is the acceleration due to gravity

Here, $\mathit{T}$depends only on length of pendulum $\mathit{L}$and gravitational acceleration $\mathit{g}$and both have fixed value. So $\mathit{T}$is constant through the SHM. Hence, we see that angular frequency is constant throughout the SHM.

Also, since ${\mathit{θ}}_{\mathbf{2}}\mathbf{=}{\mathit{θ}}_{\mathbf{1}}$at end points of the oscillation, so ${\mathit{θ}}_{\mathbf{2}}\mathbf{-}{\mathit{θ}}_{\mathbf{1}}\mathbf{=}\mathbf{0}$is minimum at end points and ${\mathit{θ}}_{\mathbf{2}}\mathbf{=}{\mathit{θ}}_{\mathbf{1}}$is maximum at equilibrium position. Hence, the angular velocity is not constant in SHM.

Therefore, Angular frequency is constant and Angular velocity is variable.