$3\mathrm{.}2\mathrm{.}10.[$Level $2]$ The collar with mass $m$ can slide freely

along the $ro\frac{d}{b}ar(AB).$ The rod is rotating at a constant rate of

${}^{}=6ra\frac{d}{s}.$ At $t=0$ the collar is located a distance $r_0$ from

A and $r^{}=0.$ You can neglect gravity. Also, the solution

to $x^{}+b^{2}x=0$ is $x(t)=a_{1}sin(bt)+a_{2}cos(bt),$ and the

solution to $x^{}-b^{2}x=0$ is $x(t)=c_{1}sinh(bt)+c_{2}cosh(bt).$

a$.$ Find the equations of motion for $m.$

b$.$ Solve for the forces exerted on the mass by the rod

as a function of time.

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E$3\mathrm{.}2\mathrm{.}10$