How is the velocity of an object in simple harmonic motion calculated?

The velocity of an object in simple harmonic motion is calculated using the equation v = ±ω√(A^2 - x^2).

Simple harmonic motion is a type of periodic motion where the restoring force is directly proportional to the displacement from equilibrium. In other words, the further the object is from its equilibrium position, the greater the force pulling it back towards the equilibrium position. This results in an oscillation or vibration around the equilibrium position.

The velocity of an object in simple harmonic motion is constantly changing as it moves back and forth. At the equilibrium position, the velocity is at its maximum, while at the maximum displacement from equilibrium, the velocity is zero. The velocity is positive when the object is moving towards the equilibrium position and negative when it is moving away from it.

The equation for the velocity of an object in simple harmonic motion is v = ±ω√(A^2 - x^2), where v is the velocity, ω is the angular frequency, A is the amplitude (maximum displacement from equilibrium), and x is the displacement from equilibrium at any given time. The ± sign indicates that the velocity can be positive or negative depending on the direction of motion.

In summary, the velocity of an object in simple harmonic motion can be calculated using the equation v = ±ω√(A^2 - x^2), which takes into account the amplitude and displacement from equilibrium at any given time.