In simple harmonic motion, where is the velocity maximum?

In simple harmonic motion, where is the velocity maximum?

• A. At the turning points
• B. At the equilibrium position
• C. Velocity is constant
• D. Velocity is zero at all times

Answer: (B)

In simple harmonic motion, velocity varies with displacement and is greatest when the mass passes through the equilibrium position. The reason is energy: the total energy stays constant, with potential energy U = 1/2 k x^2 and kinetic energy K = 1/2 m v^2. At the center x = 0, the potential energy is zero, so all the energy is kinetic, giving the maximum speed. As the object moves toward the endpoints where x = ±A, potential energy grows and kinetic energy drops, so the speed decreases to zero at the turning points, where the motion momentarily stops before reversing. Even though the acceleration is zero right at the center, the velocity there is at its maximum because the energy has been converted to motion.

In simple harmonic motion, velocity varies with displacement and is greatest when the mass passes through the equilibrium position. The reason is energy: the total energy stays constant, with potential energy U = 1/2 k x^2 and kinetic energy K = 1/2 m v^2. At the center x = 0, the potential energy is zero, so all the energy is kinetic, giving the maximum speed. As the object moves toward the endpoints where x = ±A, potential energy grows and kinetic energy drops, so the speed decreases to zero at the turning points, where the motion momentarily stops before reversing. Even though the acceleration is zero right at the center, the velocity there is at its maximum because the energy has been converted to motion.