The period of a pendulum is the time it takes the pendulum to swing back and forth once. If the only dimensional quantities that the period depends on are the acceleration of gravity, g, and the length of the pendulum, l, what combination of g and l must the period be proportional to? (Acceleration has SI units of m/s2).

T = 2pi √ L / g

We see that the period is equal to the square root of the length and the acceleration of the gravity.

Explanation:

In a simple pendulum the angular velocity is

W = √L / g

Angular velocity is related

w = 2π f

Frequency was also related

F = 1 / T

We substitute

T = 2pi √ L / g

We see that the period is equal to the square root of the length and the acceleration of the gravity.