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JEE Main 201912 JanuaryEvening Shift
Exam
JEE Main
Year
2019
Date
12 January
Shift
Evening Shift
Subject
Physics
Chapter
Oscillations

JEE Main 2019 · 12 January · Evening Shift · Physics · Oscillations

A simple harmonic motion is represented by: y = 5( 3 + 3 3 )cm The...

A simple harmonic motion is represented by:
y=5(sin⁡3\pit+3cos⁡3\pit)cmy = 5\left(\sin 3\pit + \sqrt{3}\cos 3\pit\right)cm
The amplitude and time period of the motion are:A simple harmonic motion is represented by: y = 5( 3 + 3 3 )cm The amplitude and time period of the motion are:

Options

  1. A5cm,23s5cm, \dfrac{2}{3}s
  2. B10cm,23s10cm, \dfrac{2}{3}s
  3. C5cm,32s5cm, \dfrac{3}{2}s
  4. D10cm,32s10cm, \dfrac{3}{2}s

Correct answer

B. 10cm,23s10cm, \dfrac{2}{3}s

Step-by-step solution

y=5sin⁡(3\pit)+53cos⁡(3\pit)y = 5\sin \left(3\pit\right) + 5\sqrt{3}\cos \left(3\pit\right)

A simple harmonic motion is represented by: y = 5( 3 + 3 3 )cm The amplitude and time period of the motion are:

A2=52+(53)2=102{A}^{2} = {5}^{2} + {\left(5\sqrt{3}\right)}^{2} = {10}^{2}

A=10cmA = 10cm

ω=3π\omega = 3\pi

T=2πω=23sT = \dfrac{2\pi}{\omega} = \dfrac{2}{3}s
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