... You did not do too much in 14 minutes to try it yourself but here we go:

function smooth_weapon_startup() {
while(1) {
shotgun_onscreen.pan += (mouse_force.x-shotgun_onscreen.pan/10)*time_step;
shotgun_onscreen.pan = clamp(shotgun_onscreen.pan,-5,5);
wait(1);
}
}

Not tested.