A very long rod rotates about a pivot with a constant angular velocity $.$ A bead is constrained to slide able the rod without friction. At time $t=0,$ the bead is at rest a distance $d$ away from the pivot. Its distance $r(t)$ frit the pivot at time $t$ is

$($a$)$ dsinh$(t)$

$($b$)$ dsin$(t)$

$($c$)$ dcosh$(t)$

$($d$)$ dcos$($wt$)$