Final answer:
Radial acceleration at the equilibrium position of a pendulum is calculated using the formula a_r = v^2/L, where v is the velocity determined by converting potential energy at the pendulum's highest point into kinetic energy at the bottom.
Step-by-step explanation:
The magnitude of radial acceleration for a pendulum as it passes through the equilibrium position can be determined using physics principles of circular motion and dynamics of pendulums. In the equilibrium position, all of the pendulum's motion is tangential, and the radial acceleration can be given by the equation ar = v2/L where v is the tangential velocity and L is the length of the pendulum. The tangential velocity at this point can be calculated based on the pendulum's potential energy at its highest point being converted to kinetic energy at the lowest point.
The calculation of v involves using conservation of energy, where potential energy at the height of the swing is equal to the kinetic energy at equilibrium. If the mass m of the pendulum bob, the gravitational acceleration g, and the height h from which the pendulum is released are known, the velocity v at the equilibrium can be calculated using the equation v = √(2gh). Therefore, the radial accentuation can then be evaluated using the provided pendulum's length and the calculated velocity at the bottom of the swing.