Electricity and Magnetism

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An Oscillation Composed of A Sine Wave and its Derivative


A particle is undergoing a displacement, $y$, described by a sinusoidal oscillation. The displacement is given by $y=Asin(2\pi f t+\pi/2)$ where $A$ is the amplitude of the oscillation, and $f$ is the frequency of the oscillation. The speed of the oscillation is given by the derivative of the displacement.

If the displacement at $t=0\, sec$ is $y=A$, what is the time that the velocity will be its maximum positive value, and what is the value of the velocity at that time?