A pendulum with a length of L = 2 m performs N = 2536 oscillations in a time t = 1 hour.

A pendulum with a length of L = 2 m performs N = 2536 oscillations in a time t = 1 hour. Determine the acceleration due to gravity from this data.

L = 2 m.

t = 1 h = 3600 s.

N = 2536.

g -?

The period of oscillation of the mathematical pendulum T is the time of one complete oscillation. The oscillation period of the pendulum T is determined by the formula: T = t / N, where t is the oscillation time, N is the number of oscillations.

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

t / N = 2 * P * √L / √g.

The formula for determining the acceleration of gravity will be: g = 4 * P2 * L * N2 / t2.

g = 4 * (3.14) 2 * 2 m * (2536) 2 / (3600 s) 2 = 9.785 m / s2.

Answer: the acceleration due to gravity is g = 9.785 m / s2.