To calculate the velocity of a particle in simple harmonic motion (S.H.M.), we use the derivative of the displacement function with respect to time. The displacement function given is: x=asin‌(ωt−φ) The velocity v is the first derivative of displacement x with time t : v=‌
dx
dt
Let's compute the derivative:
‌v=‌
d
dt
[asin‌(ωt−φ)]v=a‌cos(ωt−φ)⋅‌
d
dt
(ωt−φ)v=a‌cos(ωt−φ)⋅ω
‌v=aω‌cos(ωt−φ) We need to calculate this velocity at time t=‌