iOS has a powerful physics engine built in. An easy way to harness this power is by using a spring animation.

// UIView

class func animate(withDuration duration: TimeInterval,
    delay: TimeInterval,
    usingSpringWithDamping dampingRatio: CGFloat,
    initialSpringVelocity velocity: CGFloat,
    options: UIViewAnimationOptions,
    animations: () -> Void,
    completion: ((Bool) -> Void)?)

Use this method to have the two labels animate on and off the screen in a spring-like fashion. Refer to the UIView documentation to understand each of the arguments.