A mathematical pendulum with a length of ℓ = 4 m performs harmonic oscillations. For 100 s, the pendulum makes 25

| August 10, 2021 | education

A mathematical pendulum with a length of ℓ = 4 m performs harmonic oscillations. For 100 s, the pendulum makes 25 complete oscillations. What is the acceleration of gravity?

L = 4 m.

t = 100 s.

N = 25.

g -?

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

g = 4 * N ^ 2 * P ^ 2 * L / t2.

g = 4 * (25) ^ 2 * (3.14) ^ 2 * 4 m / (100 s) ^ 2 = 9.8596 m / s2.

Answer: the acceleration due to gravity is g = 9.8596 m / s2.



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