Period of ideal pendulum from length

An ideal pendulum is an object hanging on a thread. In a gravitational field it starts oscillating after being pushed out of balance. Period of pendulum oscillation does not depend on its mass.

Conditions:

1. The angle between pendulum and gravity vector is fairly small (less than 15 degrees).

2. Ideal pendulum doesn’t gain or lose any energy, so there is no friction in the system.

3. The object is small enough to be considered a material point.

4. The thread is weightless and doesn’t change its length.

Links:

1. Wikipedia, first formula.

period

The period of oscillations.

Symbol:

T

Latex:

\(T\)

Dimension:

time

length

The length of the pendulum.

Symbol:

l

Latex:

\(l\)

Dimension:

length

law

T = 2 * pi * sqrt(l / g)

Latex:

\[T = 2 \pi \sqrt{\frac{l}{g}}\]