What should be the length of a mathematical pendulum for the period of its oscillations to be equal to 1 s?

The period T of small natural oscillations of a mathematical pendulum is calculated by the formula:

T = 2п √ (L / g),

where L is the length of the thread, g is the acceleration of gravity. From the formula it follows that with an increase in the length of the thread, the period increases.

Calculating the length of the pendulum thread
If the length of the thread is known, it is easy to find the period by directly substituting the values ​​into the formula. Finding the length of a thread from a known oscillation period is a little more difficult:

you need to get rid of the root on the right side of the formula;
express the length of the thread through the period T and the acceleration of gravity g;
substitute the values ​​of the quantities and perform the calculation.
If you square both sides of the original formula, you get the equality T2 = 4n2 * (L / g).

Formula for determining thread length:

L = T2g / 4p2 = (1 s2 * 9.8 m / s2) / (4 * 3.142) = 9.8 / (4 * 9.86) = 0.248 m.

Answer: The length of the thread of a mathematical pendulum with an oscillation period of 1 s is 0.248 m.