When performing the experiment, the student received the following data: the pendulum 81 cm

When performing the experiment, the student received the following data: the pendulum 81 cm long made 50 oscillations in 90 s. What is the value of the acceleration of gravity obtained according to the results of the experiment?

L = 81 cm = 0.81 m.

n = 50.

t = 90 s.

g -?

The period of oscillation of a mathematical pendulum T is the time of one complete oscillation.

The period T of oscillations of any pendulum is determined by the formula: T = t / n, where t is time, and which the pendulum makes n – oscillations.

The period of the mathematical pendulum T is determined by another formula: T = 2 * P * √L / √g, where P is the number pi, L is the length of the pendulum, g is the acceleration of gravity.

t / n = 2 * P * √L / √g.

t ^ 2 / n ^ 2 = 4 * P ^ 2 * L / g.

g = 4 * P ^ 2 * L * n ^ 2 / t ^ 2.

g = 4 * (3.14) ^ 2 * 0.81 m * (50) ^ 2 / (90 s) ^ 2 = 9.8596 m / s2.

Answer: as a result of the experiment, the acceleration of gravity is g = 9.8596 m / s2.