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NEET PHYSICSOscillationsEasy

Question

Identify the function which represents a non-periodic motion?

A

e−ωte^{-\omega t}

B

sin⁡ωt\sin \omega t

C

sin⁡ωt+cos⁡ωt\sin \omega t + \cos \omega t

D

sin⁡(ωt+π/4)\sin(\omega t + \pi/4)

Step-by-Step Solution

  1. Definition of Periodic Motion: A function f(t)f(t) represents periodic motion if it repeats its value at regular intervals of time, i.e., f(t)=f(t+T)f(t) = f(t + T), where TT is the time period. Trigonometric functions like sine and cosine are fundamental periodic functions.
  2. Analysis of Options: sin⁡ωt\sin \omega t: This is a basic periodic function with period T=2π/ωT = 2\pi/\omega. sin⁡ωt+cos⁡ωt\sin \omega t + \cos \omega t: This represents the superposition of two periodic functions with the same frequency. It can be rewritten as 2sin⁡(ωt+π/4)\sqrt{2}\sin(\omega t + \pi/4), which is a Simple Harmonic Motion (a type of periodic motion) with period T=2π/ωT = 2\pi/\omega. sin⁡(ωt+π/4)\sin(\omega t + \pi/4): This is a sine function with a phase shift, which remains periodic with period T=2π/ωT = 2\pi/\omega. e−ωte^{-\omega t}: This is an exponential function. It represents exponential decay where the value decreases continuously towards zero as time increases. It never repeats its value. Therefore, it represents non-periodic motion.
  3. Conclusion: The function e−ωte^{-\omega t} is the only non-periodic function among the options.

Exam Context & Concepts Covered

This question aligns with the NEET PHYSICS syllabus, specifically targeting concepts from Oscillations. Mastering this topic is crucial for scoring well in the upcoming medical entrance examinations. Solving conceptually related problems will help you understand the nuances of these concepts and improve your problem-solving speed.

PHYSICSOscillationsidentifyfunctionrepresentsnonperiodicmotion

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