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JEE Main 201910 JanuaryEvening Shift
Exam
JEE Main
Year
2019
Date
10 January
Shift
Evening Shift
Subject
Physics
Chapter
Oscillations

JEE Main 2019 · 10 January · Evening Shift · Physics · Oscillations

A particle executes simple harmonic motion with an amplitude of 5cm...

A particle executes simple harmonic motion with an amplitude of 5cm5cm . When the particle is at 4cm4cm from the mean position, the magnitude of its velocity in SISI units is equal to that of its acceleration. Then, its periodic time in seconds is:

Options

  1. A8π3\dfrac{8\pi}{3}
  2. B38π\dfrac{3}{8}\pi
  3. C4π3\dfrac{4\pi}{3}
  4. D73π\dfrac{7}{3}\pi

Correct answer

A. 8π3\dfrac{8\pi}{3}

Step-by-step solution

v = \omega\sqrt{{5}^{2} - {4}^{2}} = 3\omega<br/><br/><br/><br/>a = {\omega}^{2} \times 4<br/><br/>∣a∣=∣v∣<br/><br/><br/><br/> \left|a\right| = \left|v\right| <br/><br/>4{\omega}^{2} = 3\omega<br/><br/><br/><br/>\omega = 34=2πT<br/><br/>\dfrac{3}{4} = \dfrac{2\pi}{T} <br/><br/>T = 8π3\dfrac{8\pi}{3}sec
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