During the same time, the mathematical pendulum made 40 oscillations, and the second 60.

During the same time, the mathematical pendulum made 40 oscillations, and the second 60. Determine the ratio of the length of the first to the second

Data: Nm1 – the number of oscillations of the first pendulum (Nm1 = 40 oscillations); Nm2 is the number of oscillations of the second pendulum (Nm2 = 60 oscillations); t = tm1 = tm2 is the duration of the oscillations of the pendulums.

To find out the ratio of the lengths of the taken pendulums, consider the ratio:

Nm1 * Tm1 = t = Nm2 * Tm2;

Nm1 * 2 * Π * √ (lm1 / g) = Nm2 * 2 * Π * √ (lm2 / g);

Nm1 * √lm1 = Nm2 * √lm2;

√lm1 / √lm2 = Nm2 / Nm1;

√ (lm1 / lm2) = Nm2 / Nm1;

lm1 / lm2 = (Nm2 / Nm1) 2.

Let’s perform the calculation: lm1 / lm2 = (Nm2 / Nm1) ^ 2 = (60/40) ^ 2 = 1.52 = 2.25 p.

Answer: The ratio of the lengths of the pendulums taken is 2.25 r.