Q14 of 26 Page 16

Give examples of a one-dimensional motion where

(a) the particle moving along positive x-direction comes to rest periodically and moves forward


(b) the particle moving along positive x-direction comes to rest periodically and moves backward.


Since, the question talks about periodic motion, it can be easily related to sine and cosine functions as they are periodic in nature.

(a) x = t – sin(t), this particle will move in positive x-direction if and only if t > sin(t).


When t = 0, x(t) = 0


When t = π , x(t) = π


When t = 2π , x(t) = 2π


(b) x = cos(t)


At t = 0, x(t) = 1


At t = π /2, x(t) = 0


At t = π , x(t) = -1


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