Question

Use the Buckingham Pi theorem to find the angular displacement of theta of a pendulum as a function of time (t) as well as its initial angular position theta knot. The pendulum, has a mass m and a length of rope L. To apply the theorem, you will also need the gravity (g). Please explain in detail why you got the answer you did. I'm aware this answer if already on Chegg however it got a thumbs down.

Answer 1

Buckingham Pi theorem: statement

If a physical problem involves n variables v₁…… v_n that depend on r
independent dimensional units, then the solution of the problem can
always be written in the form:

Consider a pendulum of mass m at the end of a rope of length l, and
worry about describing the displacement of the pendulum B as a
function of its initial position,

What are our variables to work with ?

How many dimensions do we need to worry about?
dimensionless
dimensionless
mass
length
length/time²
time