The ratio of the squares of the periods of oscillations of mathematical pendulums is equal to 2, which is the ratio

The ratio of the squares of the periods of oscillations of mathematical pendulums is equal to 2, which is the ratio of the lengths of these pendulums at small angles of deviation from the equilibrium position.

The oscillation period of the pendulum is determined by the formula: T = 2 * PI * root (l / g), where l is the length of the thread, g is the acceleration of gravity.
Let’s write the ratio of the squares of the periods:
T₁² / T₂² = (2 * PI * root (l₁ / g) ² / (2 * PI * root (l₂ / g)) ² = 2;
T₁² / T₂² = l₁ / l₂ = 2;
l₁ = 2 * l₂.
Answer: The ratio of the lengths of the threads is 2: 1.