One of the pendulums made 20 oscillations in some time. Another made 16 oscillations in the same time.

One of the pendulums made 20 oscillations in some time. Another made 16 oscillations in the same time. The difference in the lengths of the pendulums is 10 cm. Find the length of the second pendulum.

N = 20.

N “= 16.

t = t “.

ΔL = 10 cm.

L “-?

According to the definition, the period T is determined by the formula: T = t / N, T “= t” / N “.

t = T * N.

t “= T” * N “.

T * N = T “* N”.

Let us express the period of the mathematical pendulum T through its length: T = 2 * P * √L / √g, T “= 2 * P * √L” / √g.

2 * P * N * √L / √g = 2 * P * N “* √L” / √g.

N * √L = N “* √L”.

N ^ 2 * L = N “^ 2 * L”.

L = N “^ 2 * L” / N ^ 2.

ΔL = L “- L = L” – N “^ 2 * L” / N ^ 2 = L “* (1 – N” ^ 2 / N ^ 2).

L “= ΔL / (1 – N” ^ 2 / N ^ 2).

L “= 10 / (1 – 256/400) = 27.7 cm.

Answer: L “= 27.7 cm.