MCQ
The displacement of a particle executing SHM is given by $x=10 \sin \left(\omega t+\frac{\pi}{3}\right) \mathrm{m}$. The time period of motion is $3.14 \mathrm{~s}$. The velocity of the particle at $\mathrm{t}=0$is_________. $\mathrm{m} / \mathrm{s}$.
  • $10$
  • B
    $15$
  • C
    $20$
  • D
    $25$

Answer

Correct option: A.
$10$
a
Given,

$\mathrm{T}=3.14=\frac{2 \pi}{\omega}$

$\omega=2 \mathrm{rad} / \mathrm{s}$

$\mathrm{x}=10 \sin \left(\omega \mathrm{t}+\frac{\pi}{3}\right)$

$\mathrm{v}=\frac{\mathrm{dx}}{\mathrm{dt}}=10 \omega \cos \left(\omega \mathrm{t}+\frac{\pi}{3}\right)$

$\text { at } \mathrm{t}=0$

$\mathrm{v}=10 \omega \cos \left(\frac{\pi}{3}\right)=10 \times 2 \times \frac{1}{2}[\text { using } \omega=2 \mathrm{rad} / \mathrm{s}]$

$\mathrm{v}=10 \mathrm{~m} / \mathrm{s}$

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