If you are using UIViewPropertyAnimator the curve that you need is .easeInOut, and you can pass it as curve parameter when you create your animator:

let animator = UIViewPropertyAnimator(duration: 0.4, curve: .easeInOut) {
    // Animations
}

If you are not happy with this system curve, you can follow this answer and use this handy website to replicate FastOutSlowInInterpolator's control points.

As FastOutSlowInInterpolator documentation states:

Interpolator corresponding to fast_out_slow_in. Uses a lookup table for the Bezier curve from (0,0) to (1,1) with control points: P0 (0, 0) P1 (0.4, 0) P2 (0.2, 1.0) P3 (1.0, 1.0)

So, in your particular case you are looking for something like this:

let timingParameters = UICubicTimingParameters(
    controlPoint1: CGPoint(x: 0.4, y: 0),
    controlPoint2: CGPoint(x: 0.2, y: 1)
)
let animator = UIViewPropertyAnimator(duration: 0.4, timingParameters: timingParameters)

or this:

let animator = UIViewPropertyAnimator(
    duration: 0.4,
    controlPoint1: CGPoint(x: 0.4, y: 0),
    controlPoint2: CGPoint(x: 0.2, y: 1)
) {
    // Animations
}

SwiftUI

In SwiftUI you can animate almost any change with .animate modifier and it accepts the curve as the argument. I think .interpolatingSpring(stiffness: 30, damping: 20) is the curve that you are looking for (the bottom one).

Examples

struct ContentView: View {
    @State var isLeading = false

    var body: some View {
        VStack {
            SpacedCircle(isLeading: $isLeading)
                .animation(.linear)

            SpacedCircle(isLeading: $isLeading)
                .animation(.easeIn)

            SpacedCircle(isLeading: $isLeading)
                .animation(.easeOut)

            SpacedCircle(isLeading: $isLeading)
                .animation(.easeInOut)

            SpacedCircle(isLeading: $isLeading)
                .animation(.interactiveSpring(response: 0.27, dampingFraction: 0.5, blendDuration: 0.2))

            SpacedCircle(isLeading: $isLeading)
                .animation(.interpolatingSpring(stiffness: 30, damping: 20))

            Button("Toggle") { isLeading.toggle() }
        }
    }
}

UIKit

You can achieve that similarly in UIKit too:

Example

    @IBAction func touched(_ sender: UIButton) {
        UIView.animate(withDuration: 1, delay: 0, usingSpringWithDamping: 1, initialSpringVelocity: 3, options: []) {
            self.circleView.transform = .identity
        }
    }

    @IBAction func touchDown(_ sender: Any) {
        UIView.animate(withDuration: 1, delay: 0, usingSpringWithDamping: 1, initialSpringVelocity: 3, options: []) {
            self.circleView.transform = CGAffineTransform(translationX: 240, y: 0)
        }
    }