The body performs harmonic vibrations, which are described by the equation x = 4cos (8t – π / 4) cm

The body performs harmonic vibrations, which are described by the equation x = 4cos (8t – π / 4) cm. Determine the maximum speed of the body.

By definition, the speed of a body is equal to the first derivative of the law of motion in time:

v = x ‘.

Then we get the law for speed:

v (t) = (4cos (8t – π / 4)) ‘= 4 * 8 * (-sin (8t – π / 4) = -32sin (8t – π / 4).

It follows from the law of speed change that the maximum speed will be 32 cm / s or 0.32 m / s.

Answer: the required speed is 0.32 m / s.