Question

for a particle performing linear shm ,its average speed over one oscillation

Answer 1

a particle performing linear simple harmonic motion of time period T.

we know , time period is Time taken to complete one revolution or one oscillation.
and we know, angle made by one oscillation is 2π radians
so, average angular speed over one oscillation , $\omega$ = angular displacement/time period
= 2π/T

hence, average angular speed , $\omega=\frac{2\pi}{T}$