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_________ \(\mathrm{m} / \mathrm{s}\).

\(\mathrm{T}=3.14=\frac{2 \pi}{\omega}\)

\(\omega=2 \mathrm{rad} / \mathrm{s}\)

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

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

\(\text { at } \mathrm{t}=0\)

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

\(\mathrm{v}=10 \mathrm{~m} / \mathrm{s}\)