If the maximum speed and acceleration of a partical executing SHM is `20 cm//s and 100 cm//s`, find the time period od oscillation.

Explanation

Given `|nu_(max)| = a omega = 20 cm//s` (i)
and `|f_(max)| = a omega^(2) = 100 pi cm//s^(2)` (ii)
Dividing Eq. (ii) by Eq. (i), we get
`omega = 5 pi rad//s`
Therefore, time period
`T = (2 pi)/(omega) = (2 pi)/(5 pi) = 0.4 s`