Question: 1 Identify the function which represents a non-periodic motion.
(1) e^{-\omega t}
(2) \sin \omega t
(3) \sin \omega t+\cos \omega t
(4) \sin (\omega t+\pi / 4)
Answer: Option (1)
Explanation:
A periodic motion repeats itself after a fixed interval of time.
Functions like \sin \omega t, \cos \omega t, and their combinations repeat after a time period T=\frac{2\pi}{\omega}.
However, the function e^{-\omega t} is an exponentially decaying function.
It decreases continuously with time and never repeats its value after any regular interval.
Therefore, it represents a nonperiodic motion.