A particle is executing `SHM`. Find the positions of the particle where its speed is `8 cm//s`, if maximum magnitudes of its velocity and accleration are `10 cm//s` and `50 cm//s` respectively.

Answer

`+- (6)/(5) cm = +- 1.2 cm` from the mean position

Explanation

`|v| = |A|omega rArr 10 = |A|omega`
`|a| = |A|omega^(2) rArr 50 = |A|omega^(2)`
`rArr omega = 5 rArr |A|= 2`
`v^(2) = omega^(2)(A^(2) - x^(2))`
`8^(2) = 5^(2)(2^(2) - x^(2))`
`4 - x^(2) = (64)/(25) rArr x^(2) = (36)/(25) rArr x = +- (6)/(5) cm`