Consider the following mathematical functions of time ( t ): (I) e^ - t (II) _e( t) (III) e^ t (IV) ( t) + ( t) How many of the given functions represent non-periodic motion?

Step-by-step solution

A function represents periodic motion if it repeats its values at regular intervals of time, which requires it to be bounded and oscillatory. (I) e^ - t decreases monotonically to zero as t . It does not repeat its values, so it is non-periodic. (II) _e( t) increases monotonically with time. It is non-periodic. (III) e^ t increases exponentially with time and is unbounded. It is non-periodic. (IV) ( t) + ( t) can be rewritten as 2 ( t + 4 ) , which is a bounded, repeating trigonometric function. It represents perio