Pegged Pendulum

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58.Pegged Pendulum

+10

A bob of mass

m

hangs from a light, inextensible string of length

\ell

attached to a fixed support. A thin peg is fixed at distance

\ell/2

directly below the support. The string is held horizontal, with the bob at the height of the support, and released from rest. What is the maximum tension in the string during the subsequent motion?

$A fixed support point $P$ at the top. A light string of length $\ell$ extends horizontally to the right from $P$, ending at a small filled circle labeled $m$ (the bob at release). Label the string length "$\ell$". A small filled dot directly below $P$ at vertical distance $\ell/2$, labeled "peg". Show the vertical distance from $P$ to the peg labeled "$\ell/2$", with a thin dashed vertical line connecting them. A faint dashed arc traces the bob's initial path (radius $\ell$ about $P$) down to the lowest point directly below $P$, where a second, tighter dashed arc (radius $\ell/2$ about the peg) shows the bob continuing on the smaller circle. Mark the bob's release with a small "released from rest" annotation or a zero-velocity tick.$

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