The oscillation periods of two mathematical pendulums are in the ratio 3: 2.

The oscillation periods of two mathematical pendulums are in the ratio 3: 2. Calculate how many times the first pendulum is longer than the second.

T1 / T2 = 3/2.

L1 / L2 -?

The period of oscillation of the 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.

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 thread, g is the acceleration of gravity.

T1 = 2 * P * √L1 / √g.

L1 = T1 ^ 2 * g / 4 * P ^ 2.

T2 = 2 * P * √L2 / √g.

L2 = T2 ^ 2 * g / 4 * P ^ 2.

L1 / L2 = T12 * g * 4 * P ^ 2 / T2 ^ 2 * g * 4 * P ^ 2 = T1 ^ 2 / T2 ^ 2.

L1 / L2 = 3 ^ 2/2 ^ 2 = 9/4 = 2.25.

Answer: The length of the first pendulum is 2.25 times the length of the second pendulum.