MCQ
A particle is executing simple harmonic motion with a period of $T$ seconds and amplitude a metre. The shortest time it takes to reach a point $\frac{a}{{\sqrt 2 }}\,m$ from its mean position in seconds is
  • A
    $T$
  • B
    $T/4$
  • $T/8$
  • D
    $T/16$

Answer

Correct option: C.
$T/8$
c
(c) $y = a\sin \frac{{2\pi }}{T}t$

==> $\frac{a}{{\sqrt 2 }} = a\sin \frac{{2\pi }}{T} \cdot t$ 

==> $\sin \frac{{2\pi }}{T}t = \frac{1}{{\sqrt 2 }} = \sin \frac{\pi }{4}$

==> $\frac{{2\pi }}{T}t = \frac{\pi }{4}$

==> $t = \frac{T}{8}$

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