Oscillations · JEE Preparation Physics

Which of the following functions of time represents a simple harmonic motion?

Practice question from Oscillations (JEE Preparation Physics), with the correct answer and a step-by-step solution.

easy · MCQ · Q-682727

Which of the following functions of time represents a simple harmonic motion?

  1. A.sin(omega t) - cos(omega t)Correct answer
  2. B.sin^2(omega t)
  3. C.1 + omega t + omega^2 t^2
  4. D.e^{-omega t}

Solution

The function sin⁡(ωt)−cos⁡(ωt)\sin(\omega t) - \cos(\omega t) can be rewritten as 2sin⁡(ωt−π/4)\sqrt{2}\sin(\omega t - \pi/4), which represents a simple harmonic motion. All other options do not represent periodic or simple harmonic motion.

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