Question

A wire frame in the shape of an equilateral triangle is hinged at one vertex so that it can swing freely in a vertical plane with the plane of the triangle always remaining vertical the side of the frame is 1 by root 3 m the time period in seconds of small oscillations of the frame will be

Answer 1

The side of frame is 1/√3
so, altitude of equilateral triangle , l = √{a² - (a/2)²} = √3a/2 , where a is side length of the equilateral triangle.
= √3 × (1/√3)/2 = 0.5 m

now, use formula of simple pendulum,
$T=2\pi\sqrt{\frac{l}{g}}$

= 2π√{0.5/10}

= 2π√(0.05)

= 2π × 2.236/10

= 2 × 3.14 × 0.236

= 1.482 sec

hence time period of oscillation= 1.482sec