Two pendulums are deflected from their equilibrium position and are simultaneously released.

Two pendulums are deflected from their equilibrium position and are simultaneously released. The first pendulum with a suspension length of 4 m performed 15 oscillations in a certain period of time. The second one made 10 oscillations during the same time. How long is the second pendulum?

The values of a pendulum with a length of 4 m will be denoted by indices 4, a pendulum with an unknown length – by indices x.

Pendulum oscillation periods:

T4 = 2П√ (l4 / g);

Tx = 2П√ (lx / g) (l4, lx are the lengths of the pendulums, g is the acceleration of gravity).

The number of oscillations of the pendulums for the same time t:

n4 = t / (2П√ (l4 / g)) = 15;

nx = t / (2П√ (lx / g)) = 10.

We divide the penultimate equality by the last one:

(t / (2П√ (l4 / g))) / (t / (2П√ (lx / g))) = 1.5;

√lx / √l4 = 1.5;

√lx = 1.5√l15;

lx = 2.25 * l4;

lx = 2.25 * 4 m = 10 m.

Answer: 10 m.