A compound pendulum for a large clock has the geometry shown. Consider the arm to be a

slender rod, i$.$e$.J_G=\frac{1}{12}{m}_{\text{a}\text{r}\text{m}}{L}^2.$ The polar mass moment of inertia of the bob about its center of

mass is$,J_G=\frac{1}{12}{m}_{\text{b}\text{o}\text{b}}(a^2+b^2).$ The distance from the pivot point to the center of mass of the bob

is$,d=L+\frac{a}{2}.$

$a=0\mathrm{.}5m,b=0\mathrm{.}08m,m_{\text{b}\text{o}\text{b}}=70kg,$

$m_{\text{a}\text{r}\text{m}}=1\mathrm{.}5kg,L=0\mathrm{.}7m.$

a$)$ What is the period, $,$ of the

pendulum?

b$)$ Find the Center of Percussion of

the compound pendulum