How is velocity calculated in oscillatory motion?

Velocity in oscillatory motion is calculated using the derivative of displacement with respect to time.

In oscillatory motion, an object moves back and forth around a central point, with its displacement changing periodically. The velocity of the object at any given point in time is the rate of change of its displacement with respect to time. This can be expressed mathematically as:

v = d/dt (x)

where v is the velocity, x is the displacement, and d/dt represents the derivative with respect to time.

For simple harmonic motion, where the displacement of the object follows a sinusoidal pattern, the velocity can be expressed as:

v = -Aωsin(ωt + φ)

where A is the amplitude of the motion, ω is the angular frequency, t is the time, and φ is the phase angle. The negative sign indicates that the velocity is in the opposite direction to the displacement.

The maximum velocity occurs at the equilibrium position, where the displacement is zero. At this point, the velocity is equal to the product of the amplitude and the angular frequency:

v_max = Aω

The velocity is also zero at the turning points, where the displacement is at its maximum.

In summary, the velocity in oscillatory motion is calculated using the derivative of displacement with respect to time, and for simple harmonic motion, it can be expressed as a sinusoidal function of time.