In on edimensional motion, the displacement of the particle in periokic motion must be linked with sine or cosing function. The particle will be moving alon + ive x-direction only if ` t gt sin t`. Hence,
` x (t) =- t - sin t`.
Velocity, ` v (t) = (dx0 (t) 0/(dt) =1- cso t` and acceleration, `a (t) = (dv)/(dt) = sint`
`v (t) =0, when ` t= 0 or 2 pi and a (t) =0`.
Whem ` t = pi`, dospacement, `x (t) = pi - sin pi = pi (poritive)`
Whem ` t = 2 pi`, dospacement, `x (t) = pi - sin pi = pi (poritive)`
(b) In one dimensional motion, where a particle moving along positive x-direction comes to rest preiodically an dmoves bachward can be represented by ` x (t) = sin t`.
Here, ` v = (dx)/(dt) = cos t`
acceleration, `a = (dv)/(dt) =- sin t`
When ` t=0, x =0, v =positive, a =0`
When ` t= pi //2`, x= + ive, v=0, a=- ve
When ` t= -pi, x=0, v=- ve, a=0`
When ` t= 3 pi //2, x =- ive, v=- 0, a= + ive`
When ` 1= 2 pi , x =0 , v= + ve , a=0`.
