During the same time period, the first pendulum made 10 oscillations, and the second 20.

During the same time period, the first pendulum made 10 oscillations, and the second 20. Compare the lengths of the pendulums.

t1 = t2.

N1 = 10.

N2 = 20.

g = 10 m / s2.

L1 / L2 -?

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 time during which the pendulum makes N complete oscillations.

T1 = t1 / N1.

T2 = t2 / N2.

The period of the mathematical pendulum T is determined by the formula: T = 2 * P * √L / √g, where P are the numbers pi, L is the length of the pendulum’s thread, g is the acceleration of gravity.

T1 = 2 * P * √L1 / √g.

t1 / N1 = 2 * P * √L1 / √g.

t12 / N1 ^ 2 = 4 * P ^ 2 * L1 / g.

L1 = g * t1 ^ 2/4 * P ^ 2 * N1 ^ 2.

L2 = g * t2 ^ 2/4 * P ^ 2 * N2 ^ 2.

L1 / L2 = 4 * P ^ 2 * N ^ 2 * g * t1 ^ 2 / g * t2 ^ 2 * 4 * P ^ 2 * N1 ^ 2 = N2 ^ 2 / N1 ^ 2.

L1 / L2 = (20) ^ 2 / (10) ^ 2 = 4.

Answer: the length of the first pendulum is 4 times the length of the second pendulum L1 / L2 = 4.