# 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.