A uniform rectangular sign of width 53.4 cm, height 31.4 cm

Question

A uniform rectangular sign of width 53.4 cm, height 31.4 cm, and negligible thickness hangs vertically from supporting hinges attached at its upper edge. Find the period of small-amplitude oscillations of the sign.

Answer 1

This is a pendulum problem with the sign's center of mass,  where all it's weight can be considered to be concentrated.  The formula for pendulum period is

 

                          T = 2pi (L/g) ^1/2

 

The exponential 1/2 means take the square root of L/g.  In this case L = 0.5 times (0.314) and g = 9.8.  Neither the width nor the mass matter as they do no appear in the formula.  Notice that 31.4 cm had to be converted to 0.34 m in order for the units to come out right.