Help with physics question,?

Question

A mass is swung on a string of length L. The mass makes one revolution in T seconds. Calculate the angle (theta) that the string makes with the vertical, in terms of g, L, and T.

Answer 1

We'll need two formulas.

T = 2π sqrt(L/g)
θ = θo * sin[ sqrt(g/L) t ]

θo is the initial angle made with the vertical (we're assuming it's small... less than 10º)

To make things easy, let's give a definition...
ω = sqrt(g/L)

T = 2π / ω
θ = θo * sin[ ω t ]

So ω = 2π / T, and

θ = θo * sin[ 2π t / T ]


Notice our final result only depends on g and L in the sense that T depends on g and L.


I hope I've answered your question. The question seemed a little vague.