The displacement x(t) of a particle moving along a straight line is given by various mathematical functions of time t . Which of the following functions represents a motion that is NOT periodic?

Step-by-step solution

For a function to represent periodic motion, it must repeat its values after a regular interval of time. Option (A): x(t) = A ^3( t) = A 4 (3 ( t) - (3 t)) . This is a sum of periodic functions, hence it is periodic. Option (B): x(t) = A ( t) + B ( t) = A^2+B^2 ( t + ) . This represents simple harmonic motion, which is periodic. Option (C): x(t) = A ( t) . The logarithmic function is strictly increasing for t > 0 and never repeats its values. Hence, it is not periodic. Option (D): x(t) = A ^2( t) = A 2 (1 + (2 t))