Determine the length of the thread pendulum if it makes 5 oscillations during 10 s.

We start by recording given:

t = 10 s;

n = 5;

g = 9.8 m / s ^ 2 – acceleration of gravity.

L -?

Solution:

Let us calculate the period of oscillation of the pendulum by the formula:

T = t / n;

Substitute the values and find:

T = 10/5 = 2 s.

Let us recall the formula for the oscillation period of a mathematical pendulum:

T = 2π * √ (L / g).

We square both sides of the formula:

T ^ 2 = 4 * π ^ 2 * L / g.

We obtain the formula for calculating the length of the thread of a mathematical pendulum:

L = g * T ^ 2 / (4 * π ^ 2).

L = 9.8 * 2 ^ 2 / (4 * 3.14 ^ 2) ≈ 1 m.