Determine the length of the thread pendulum if its oscillation frequency is 0.2 Hz.

To solve this task, let us remember what the period of oscillation of the pendulum is if its length is known;

T = 2 * P * √ (l * g);

Where;

T is the period of oscillation of the pendulum;

P – number “Pi” equal to 3.14;

l is the length of the pendulum;

g – acceleration due to gravity, equal to 9.8 m / s2;

From this formula, we express the length and get the following expression;

l = T2 * g / (4 * P2);

Let us write down the formula for the dependence of the period on the oscillation frequency;

T = 1 / f;

Knowing the frequency, we find the period;

T = 1 / 0.2 = 5;

Substitute the received data into the formula;

l = 52 * 9.8 / (4 * 3.142);

l = 25 * 9.8 / 4 * 9.8 = 25/4 = 6.25m.

Answer: Length l = 6.25m.