A particle executed SHM amplitude 20cm and tme period 4s. What is minimum time required for the particle to move between two points 10cm on either side of mean position?

Explanation

If the particle starts from mean position, its displacement at instant t is given by ,br> `y = A sin omegat`
Here, ` A = 20 cm, T = 2 s, y = 10 cm`
`omega = (2pi)/(T) = (2pi)/(2) = pi` rad/s
`10 = 20 sin omegat `
` rArr (1)/(2) = sin omegat`
`rArr pit = sin^(-1)((1)/(2)) = (pi)/(6)`
`rArr t = (1)/(6)s`
So, the time taken by the particle to move between two points 10 cm on either side of the mean position is given by
`2t = 2 xx (1)/(6) = (1)/(3) s = 0.33s`