The displacement of a particle executing SHM is given by x = 10 sin ( wt + 3 π ) m . The time period of motion is 3.14 s . The velocity of the particle at t = 0 is ______ m / s .

Question

The displacement of a particle executing SHM is given by x = 10 sin ( wt + 3 π ​ ) m . The time period of motion is 3.14 s . The velocity of the particle at t = 0 is ______ m / s .

TestHub · Accepted Answer

Given, ​ T = 3.14 = ω 2 π ​ ω = 2 rad / s x = 10 sin ( ω t + 3 π ​ ) v = dt dx ​ = 10 ω cos ( ω t + 3 π ​ ) at t = 0 v = 10 ω cos ( 3 π ​ ) = 10 × 2 × 2 1 ​ [ using ω = 2 rad / s ] v = 10 m / s ​

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