Question

The displacement equation of a particle given by the equation Y = A sin(wt) The maximum particle velocity is​

Answer 1

Answer:

Maximum velocity = Aω

Explanation:

Y = A sin(ωt)

dY/dt = Aω cos(ωt)

∴ v = Aω cos(ωt)

For maximum velocity cos(ωt) = 1

∴ Maximum velocity = Aω

Answer 2

Answer:

Maximum velocity is Aω.

Explanation:

The displacement equation of a particle given by the equation Y = A sin(ωt)

We need to find the maximum particle velocity.

Displacement is the shortest distance from the initial to the final position. It is a vector quantity.

Velocity is defined as rate of change of displacement. It is a vector quantity.

Since, Y = A sin(ωt)

Differentiating it, we get

dY/dt = Aω cos(ωt)

Therefore velocity is  v = Aω cos(ωt)

Fir maximum velocity  cos(ωt) = 1

Hence, Maximum velocity = Aω

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