Question

A compound pendulum consists of a 1.35-m stick pivoted at a small hole drilled at a distance d from the middle of the stick. If the period of oscillation is 3.60 s, find d.

Incorrect

Answer 1

Period of oscillation for phsical pendulum,

T = 2*sqrt (l / mgd)

l = T^2*mgd / 4^2 .......(1)

From principal axis theorem,

l = lo + mr^2

l = (1/12)mL^2 + md^2 ......(2)

From eq (1) and (2),

T^2*mgd / 4^2 = (1/12)mL^2 + md^2

(1/12)L^2 + d^2 = T^2 *g d / 4^2

(1/12)*(1.35)^2 + d^2 = (3.6)^2 * 9.8*d / 4^2

d^2 - 3.217d + 0.1518 = 0

By solving the quadratic equation,

d = 3.169 m or 0.0479 m

so, d = 0.0479 m