MCQ
A particle executing $S.H.M.$ of amplitude 4 cm and $T = 4 \,sec.$ The time taken by it to move from positive extreme position to half the amplitude is ..... $\sec$
  • A
    $1$
  • B
    $0.33$
  • $0.67$
  • D
    $1.22$

Answer

Correct option: C.
$0.67$
c
(c) Equation of motion $y = a\cos \omega t$

$\frac{a}{2} = a\cos \omega t$

$\Rightarrow \cos \omega t = \frac{1}{2}$

$\Rightarrow \omega t = \frac{\pi }{3}$

$ \Rightarrow \frac{{2\pi t}}{T} = \frac{\pi }{3}$

$\Rightarrow t = \frac{{\frac{\pi }{3} \times T}}{{2\pi }} = \frac{4}{{3 \times 2}} = \frac{2}{3}\sec $

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