One of the 2 mathematical pendulums made 8 oscillations in some time. Another made 6 vibrations during the same time.

One of the 2 mathematical pendulums made 8 oscillations in some time. Another made 6 vibrations during the same time. The difference in the lengths of the pendulums is 14 cm. Find the length of the first pendulum. the answer is in centimeters.

N1 = 8.

N2 = 6.

t1 = t2.

l2 – l1 = 14 cm = 0.14 m.

g = 10 m / s2.

l1 -?

The period of the mathematical pendulum T is determined by the formulas: T = t / N and T = 2 * P * √l.

/ √g.

t1 / N1 = 2 * P * √l1 / √g.

t1 = 2 * P * N1 * √l1 / √g.

t2 / N2 = 2 * P * √l2 / √g.

t2 = 2 * P * N2 * √l2 / √g.

2 * P * N1 * √l1 / √g = 2 * P * N2 * √l2 / √g.

N1 * √l1 = N2 * √l2.

l1 = N2 ^ 2 * l2 / N12.

l1 = N2 ^ 2 * (l1 + 0.14) / N12.

l1 * N1 ^ 2 = N2 ^ 2 * (l1 + 0.14).

l1 * N1 ^ 2 = N2 ^ 2 * l1 + 0.14 * N2 ^ 2.

l1 * N1 ^ 2 – N2 ^ 2 * l1 = 0.14 * N2 ^ 2.

l1 = 0.14 * N2 ^ 2 / (N1 ^ 2 – N2 ^ 2).

l1 = 0.14 * (6) ^ 2 / ((8) ^ 2 – (6) ^ 2) = 0.18 m = 18 cm.

Answer: the length of the first mathematical pendulum is l1 = 18 cm.