Question

Dimensional Analysis: Often, we can almost derive formulas (up to an overall constant) just by knowing the units of the relevant quantities. Under the assumption that the pendulum's period can only depend on the pendulum's length L, m, maximum angle 0, and the strength of gravity g (with units [g]=m/s2), explain why we must have a relation like mass L T f(0) (Note that 0 counts as a unitless parameter here.) Asserting f(0)~ f(0) in this formula is the small X 9 angle approximation (where f(0) = 27 is found by other means)

Answer 1

T= flox F comparing both sides on the basis of dimension L.His = [T] = Tr0 [9] = {@J= 172 Rilis = [ {10)» g=[FJELV ]"? [T2J$-7-@ from ① & ② it is clear that form of I must have ITX