The displacement of a particle executing SHM is given by . The time period of motion is 3.14s. The velocity of the particle at is _______ m/s.

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Solution

Q.
The displacement of a particle executing SHM is given by $x = 10$ $\sin (ω t + \frac{π}{3}) m$ . The time period of motion is 3.14s. The velocity of the particle at $t = 0$ is _______ m/s. [2024]

Ans.
(10)    $x = 10 \sin (ω t + \frac{π}{3})$

$ω = \frac{2 π}{T} = \frac{2 π}{3.14} = 2 rad / s$

   $at t = 0, x = 10 s i n \frac{π}{3} = 5 \sqrt{3} m$

   $n o w v = ω \sqrt{(A^{2} - x^{2})} = 2 \sqrt{10^{2} - {(5 \sqrt{3})}^{2}}$

$v = 2 \sqrt{100 - 75} = 10 m / s$

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