Figure P$2\mathrm{.}76$

$2\mathrm{.}76$ A particle $P$ of mass $m$ moves on a smooth, hori$-$

zontal table and is attached to a light, inextensible cord

that is being pulled downward by a force $F(t)$ as shown in

Figure P$2\mathrm{.}76.$ Show that the differential equations of mo$-$

tion of $P$ are

$-F=m((vec(r))-r{}^{}{?}^2)$

$0=r{}^{}+2r^{}{}^{}$

Then show that Equation $(2)$ implies that $r^2{}^{}=$ constant.