Question

A massless isosceles triangle hangs in a homogeneous gravitational field g at suspension point A, two point masses m are placed at two other corners (as shown in Figure). The height of the triangle is h; the length of the two same edges is l. The triangle swings without friction around the suspension point. The period of the vibration is given by: T = 211 Mes where I A is the moment of inertia relative to the suspension point A, ras is the distance between suspension point A and center of mass of the triangle, and M the total mass of the triangle as a physical pendulum. 1) Unter what condition/boundary does the above formula for T hold? 2) Calculate the period T as a function of m, h, I and g. 3) Why the period T diverges, as h→0? 4) Determine h, when the triangle can be regarded as a mathematical pendulum. What is the formula for period T in this case?

Answer 1

ปีน - (1) Amplitude AM of vibration in mall. (2) T= 21 JA 1A = ml tme v Mgr AS Mmmm m+ m2 "As' = 2 h 3 licentre of man leson The com hrad 2me2 2. T: 2h :: 7-21 rent zaje Bizielo vg (3) We can see I diverges as h tends too because when he tends to zero there wont be any moment of force driving the semiple hou mnie notion and the neoties will be Prieten (4) for a mathemali col pendula > 2 ne = 20 =) h= forhol T- Scanned with CamScanner Vol. 2 ñ ex b VV =ant VE8