One of the two mathematical pendulums made 10 oscillations, and the other during the same time – 6 oscillations.

| March 19, 2021 | education

One of the two mathematical pendulums made 10 oscillations, and the other during the same time – 6 oscillations. the difference in the lengths of the pendulums is 16 cm. Determine the lengths of the pendulums.

N1 = 10.

N2 = 6.

t1 = t2 = t.

ΔL = 16 cm.

L1 -?

L2 -?

The period of the mathematical pendulum T is determined by the formula: T1 = t1 / N1 = t / N1,

T2 = t2 / N2 = t / N2.

t = T1 * N1.

t = T2 * N2.

T1 * N1 = T2 * N2.

The period of a mathematical pendulum is determined by another formula: T1 = 2 * п * √L1 / √g, T2 = 2 * п * √L2 / √g.

2 * п * N1 * √L1 / √g = 2 * п * N2 * √L2 / √g.

N1 * √L1 = N2 * √L2.

N1 ^ 2 * L1 = N2 ^ 2 * L2.

L1 = N2 ^ 2 * L2 / N1 ^ 2.

ΔL = L2 – L1 = L2 – N2 ^ 2 * L2 / N1 ^ 2 = L2 * (1 – N2 ^ 2 / N1 ^ 2).

L2 = ΔL / (1 – N2 ^ 2 / N1 ^ 2).

L2 = ΔL / (1 – N2 ^ 2 / N1 ^ 2).

L2 = 16 / (1 – 36/100) = 25 cm.

L1 = L2 – ΔL.

L1 = 25 cm – 16 cm = 9 cm.

Answer: L2 = 25 cm, L1 = 9 cm.



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