Can someone tell me what would be the math required for moving around the small ball in the bar(meter) according to the touch motion…. I needed a clear idea on the logic..

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The logic depends on how you want to model the interaction between the finger and the ball. Is it moving through a fluid, like a ball bearing? A gravitational field? Do you want it to decelerate as if under the influence of friction from the sides of the bar? Or do you want to simply have the ball track the finger, without fancy damping of the motion?
My point is that the “logic” can be pretty complicated, depending on how you decide to model it. I’d recommend looking for something canned in JavaScript before coding it yourself.