Question

for the oscillating pendulum, at which point in its path does it reach its maximum velocity? at which point does it reach its maximum acceleration? session

Answer 1

The maximum velocity of an oscillating pendulum occurs at the equilibrium position (x = 0), while the maximum acceleration occurs at the maximum displacement from equilibrium (x = ±A). These maxima are described by formulas incorporating the amplitude and the angular frequency of the pendulum's motion.

Step-by-step explanation:

For an oscillating pendulum, which functions under the principles of Simple Harmonic Motion (SHM), the point at which it reaches its maximum velocity is at the equilibrium position, denoted as x = 0. At this point, all of the energy of the system is kinetic, and there is no potential energy in the pendulum. Hence, the pendulum's velocity is greatest as it passes through this point regardless of the direction.

The point at which the pendulum achieves its maximum acceleration is at the extremes of its motion, where the displacement is x = ±A (A represents the amplitude of the motion). Here, the pendulum changes its direction, and the acceleration vector is at its peak magnitude, as the restoring force, and thus the acceleration, is the greatest.

The formula for maximum velocity (
`U_{max`). in SHM is directly proportional to the amplitude (A) and the angular frequency (ω). Similarly, the maximum acceleration (
`a_{max`) is also proportional to the amplitude and the square of the angular frequency (ω²).