Gist for http://castorflex.github.io/blog/2013/04/12/making-a-bounce-animation-for-your-sliding-menu/

CustomBounceInterpolator.java

import android.view.animation.Interpolator;

/**
 * Created with IntelliJ IDEA, best IDE in the world. User: castorflex Date: 06/06/13 Time: 22:18
 */
public class CustomBounceInterpolator implements Interpolator {

    @Override
    public float getInterpolation(float t) {
        return -(float) Math.abs(Math.sin((float) Math.PI * (t + 1) * (t + 1)) * (1 - t));
    }
}

CustomScroller.java

import android.content.Context;
import android.hardware.SensorManager;
import android.os.Build;
import android.util.FloatMath;
import android.view.ViewConfiguration;
import android.view.animation.AnimationUtils;
import android.view.animation.Interpolator;

/**
 * Created with IntelliJ IDEA, best IDE in the world. User: castorflex Date: 08/05/13 Time: 11:33
 */
public class CustomScroller {
    private int mMode;

    private int mStartX;
    private int mStartY;
    private int mThresholdX;
    private int mThresholdY;
    private int mFinalX;
    private int mFinalY;

    private int mMinX;
    private int mMaxX;
    private int mMinY;
    private int mMaxY;

    private int mCurrX;
    private int mCurrY;
    private long mStartTime;
    private int mDuration;
    private float mDurationReciprocal;
    private float mDeltaX;
    private float mDeltaY;
    private boolean mFinished;
    private Interpolator mInterpolator;
    private boolean mFlywheel;

    private float mVelocity;
    private float mCurrVelocity;
    private int mDistance;

    private float mFlingFriction = ViewConfiguration.getScrollFriction();

    private static final int DEFAULT_DURATION = 250;
    private static final int SCROLL_MODE = 0;
    private static final int FLING_MODE = 1;

    private static float DECELERATION_RATE = (float) (Math.log(0.78) / Math.log(0.9));
    private static final float INFLEXION = 0.35f; // Tension lines cross at (INFLEXION, 1)
    private static final float START_TENSION = 0.5f;
    private static final float END_TENSION = 1.0f;
    private static final float P1 = START_TENSION * INFLEXION;
    private static final float P2 = 1.0f - END_TENSION * (1.0f - INFLEXION);

    private static final int NB_SAMPLES = 100;
    private static final float[] SPLINE_POSITION = new float[NB_SAMPLES + 1];
    private static final float[] SPLINE_TIME = new float[NB_SAMPLES + 1];

    private float mDeceleration;
    private final float mPpi;

    // A context-specific coefficient adjusted to physical values.
    private float mPhysicalCoeff;

    static {
        float x_min = 0.0f;
        float y_min = 0.0f;
        for (int i = 0; i < NB_SAMPLES; i++) {
            final float alpha = (float) i / NB_SAMPLES;

            float x_max = 1.0f;
            float x, tx, coef;
            while (true) {
                x = x_min + (x_max - x_min) / 2.0f;
                coef = 3.0f * x * (1.0f - x);
                tx = coef * ((1.0f - x) * P1 + x * P2) + x * x * x;
                if (Math.abs(tx - alpha) < 1E-5) break;
                if (tx > alpha) x_max = x;
                else x_min = x;
            }
            SPLINE_POSITION[i] = coef * ((1.0f - x) * START_TENSION + x) + x * x * x;

            float y_max = 1.0f;
            float y, dy;
            while (true) {
                y = y_min + (y_max - y_min) / 2.0f;
                coef = 3.0f * y * (1.0f - y);
                dy = coef * ((1.0f - y) * START_TENSION + y) + y * y * y;
                if (Math.abs(dy - alpha) < 1E-5) break;
                if (dy > alpha) y_max = y;
                else y_min = y;
            }
            SPLINE_TIME[i] = coef * ((1.0f - y) * P1 + y * P2) + y * y * y;
        }
        SPLINE_POSITION[NB_SAMPLES] = SPLINE_TIME[NB_SAMPLES] = 1.0f;

        // This controls the viscous fluid effect (how much of it)
        sViscousFluidScale = 8.0f;
        // must be set to 1.0 (used in viscousFluid())
        sViscousFluidNormalize = 1.0f;
        sViscousFluidNormalize = 1.0f / viscousFluid(1.0f);

    }

    private static float sViscousFluidScale;
    private static float sViscousFluidNormalize;

    /**
     * Create a Scroller with the default duration and interpolator.
     */
    public CustomScroller(Context context) {
        this(context, null);
    }

    /**
     * Create a Scroller with the specified interpolator. If the interpolator is
     * null, the default (viscous) interpolator will be used. "Flywheel" behavior will
     * be in effect for apps targeting Honeycomb or newer.
     */
    public CustomScroller(Context context, Interpolator interpolator) {
        this(context, interpolator,
                context.getApplicationInfo().targetSdkVersion >= Build.VERSION_CODES.HONEYCOMB);
    }

    /**
     * Create a Scroller with the specified interpolator. If the interpolator is
     * null, the default (viscous) interpolator will be used. Specify whether or
     * not to support progressive "flywheel" behavior in flinging.
     */
    public CustomScroller(Context context, Interpolator interpolator, boolean flywheel) {
        mFinished = true;
        mInterpolator = interpolator;
        mPpi = context.getResources().getDisplayMetrics().density * 160.0f;
        mDeceleration = computeDeceleration(ViewConfiguration.getScrollFriction());
        mFlywheel = flywheel;

        mPhysicalCoeff = computeDeceleration(0.84f); // look and feel tuning
    }

    /**
     * The amount of friction applied to flings. The default value
     * is {@link ViewConfiguration#getScrollFriction}.
     *
     * @param friction A scalar dimension-less value representing the coefficient of
     *         friction.
     */
    public final void setFriction(float friction) {
        mDeceleration = computeDeceleration(friction);
        mFlingFriction = friction;
    }

    private float computeDeceleration(float friction) {
        return SensorManager.GRAVITY_EARTH   // g (m/s^2)
                * 39.37f               // inch/meter
                * mPpi                 // pixels per inch
                * friction;
    }

    /**
     *
     * Returns whether the scroller has finished scrolling.
     *
     * @return True if the scroller has finished scrolling, false otherwise.
     */
    public final boolean isFinished() {
        return mFinished;
    }

    /**
     * Force the finished field to a particular value.
     *
     * @param finished The new finished value.
     */
    public final void forceFinished(boolean finished) {
        mFinished = finished;
    }

    /**
     * Returns how long the scroll event will take, in milliseconds.
     *
     * @return The duration of the scroll in milliseconds.
     */
    public final int getDuration() {
        return mDuration;
    }

    /**
     * Returns the current X offset in the scroll.
     *
     * @return The new X offset as an absolute distance from the origin.
     */
    public final int getCurrX() {
        return mCurrX;
    }

    /**
     * Returns the current Y offset in the scroll.
     *
     * @return The new Y offset as an absolute distance from the origin.
     */
    public final int getCurrY() {
        return mCurrY;
    }

    /**
     * Returns the current velocity.
     *
     * @return The original velocity less the deceleration. Result may be
     * negative.
     */
    public float getCurrVelocity() {
        return mMode == FLING_MODE ?
                mCurrVelocity : mVelocity - mDeceleration * timePassed() / 2000.0f;
    }

    /**
     * Returns the start X offset in the scroll.
     *
     * @return The start X offset as an absolute distance from the origin.
     */
    public final int getStartX() {
        return mStartX;
    }

    /**
     * Returns the start Y offset in the scroll.
     *
     * @return The start Y offset as an absolute distance from the origin.
     */
    public final int getStartY() {
        return mStartY;
    }

    /**
     * Returns where the scroll will end. Valid only for "fling" scrolls.
     *
     * @return The final X offset as an absolute distance from the origin.
     */
    public final int getThresholdX() {
        return mThresholdX;
    }

    /**
     * Returns where the scroll will end. Valid only for "fling" scrolls.
     *
     * @return The final Y offset as an absolute distance from the origin.
     */
    public final int getThresholdY() {
        return mThresholdY;
    }

    /**
     * Call this when you want to know the new location.  If it returns true,
     * the animation is not yet finished.  loc will be altered to provide the
     * new location.
     */
    public boolean computeScrollOffset() {
        if (mFinished) {
            return false;
        }

        int timePassed = (int)(AnimationUtils.currentAnimationTimeMillis() - mStartTime);

        if (timePassed < mDuration) {
            switch (mMode) {
                case SCROLL_MODE:
                    float x = timePassed * mDurationReciprocal;

                    if (mInterpolator == null)
                        x = viscousFluid(x);
                    else
                        x = mInterpolator.getInterpolation(x);

                    mCurrX = mStartX + Math.round(x * mDeltaX);
                    mCurrY = mStartY + Math.round(x * mDeltaY);
                    break;
                case FLING_MODE:
                    final float t = (float) timePassed / mDuration;
                    final int index = (int) (NB_SAMPLES * t);
                    float distanceCoef = 1.f;
                    float velocityCoef = 0.f;
                    if (index < NB_SAMPLES) {
                        final float t_inf = (float) index / NB_SAMPLES;
                        final float t_sup = (float) (index + 1) / NB_SAMPLES;
                        final float d_inf = SPLINE_POSITION[index];
                        final float d_sup = SPLINE_POSITION[index + 1];
                        velocityCoef = (d_sup - d_inf) / (t_sup - t_inf);
                        distanceCoef = d_inf + (t - t_inf) * velocityCoef;
                    }

                    mCurrVelocity = velocityCoef * mDistance / mDuration * 1000.0f;

                    mCurrX = mStartX + Math.round(distanceCoef * (mThresholdX - mStartX));
                    // Pin to mMinX <= mCurrX <= mMaxX
                    mCurrX = Math.min(mCurrX, mMaxX);
                    mCurrX = Math.max(mCurrX, mMinX);

                    mCurrY = mStartY + Math.round(distanceCoef * (mThresholdY - mStartY));
                    // Pin to mMinY <= mCurrY <= mMaxY
                    mCurrY = Math.min(mCurrY, mMaxY);
                    mCurrY = Math.max(mCurrY, mMinY);

                    //As we are waiting for the end of the animation,
                    //we don't want to stop if we reach the threshold
//                    if (mCurrX == mThresholdX && mCurrY == mThresholdY) {
//                        mFinished = true;
//                    }

                    break;
            }
        }
        else {
            mCurrX = mFinalX;
            mCurrY = mFinalY;
            mFinished = true;
        }
        return true;
    }

    /**
     * Start scrolling by providing a starting point and the distance to travel.
     * The scroll will use the default value of 250 milliseconds for the
     * duration.
     *
     * @param startX Starting horizontal scroll offset in pixels. Positive
     *        numbers will scroll the content to the left.
     * @param startY Starting vertical scroll offset in pixels. Positive numbers
     *        will scroll the content up.
     * @param dx Horizontal distance to travel. Positive numbers will scroll the
     *        content to the left.
     * @param dy Vertical distance to travel. Positive numbers will scroll the
     *        content up.
     */
    public void startScroll(int startX, int startY, int dx, int dy) {
        startScroll(startX, startY, dx, dy, DEFAULT_DURATION);
    }

    /**
     * Start scrolling by providing a starting point and the distance to travel.
     *
     * @param startX Starting horizontal scroll offset in pixels. Positive
     *        numbers will scroll the content to the left.
     * @param startY Starting vertical scroll offset in pixels. Positive numbers
     *        will scroll the content up.
     * @param dx Horizontal distance to travel. Positive numbers will scroll the
     *        content to the left.
     * @param dy Vertical distance to travel. Positive numbers will scroll the
     *        content up.
     * @param duration Duration of the scroll in milliseconds.
     */
    public void startScroll(int startX, int startY, int dx, int dy, int duration) {
        startScroll(startX, startY, dx, dy, duration, startX + dx, startY + dy);
    }


    /**
     * Start scrolling by providing a starting point and the distance to travel, with a finalPosition.
     *
     * @param startX Starting horizontal scroll offset in pixels. Positive
     *        numbers will scroll the content to the left.
     * @param startY Starting vertical scroll offset in pixels. Positive numbers
     *        will scroll the content up.
     * @param dx Horizontal distance to travel. Positive numbers will scroll the
     *        content to the left.
     * @param dy Vertical distance to travel. Positive numbers will scroll the
     *        content up.
     * @param duration Duration of the scroll in milliseconds.
     */
    public void startScroll(int startX, int startY, int dx, int dy, int duration, int finalX, int finalY) {
        mMode = SCROLL_MODE;
        mFinished = false;
        mDuration = duration;
        mStartTime = AnimationUtils.currentAnimationTimeMillis();
        mStartX = startX;
        mStartY = startY;
        mThresholdX = startX + dx;
        mThresholdY = startY + dy;
        mDeltaX = dx;
        mDeltaY = dy;
        mDurationReciprocal = 1.0f / (float) mDuration;
        mFinalX = finalX;
        mFinalY = finalY;
    }

    /**
     * Start scrolling based on a fling gesture. The distance travelled will
     * depend on the initial velocity of the fling.
     *
     * @param startX Starting point of the scroll (X)
     * @param startY Starting point of the scroll (Y)
     * @param velocityX Initial velocity of the fling (X) measured in pixels per
     *        second.
     * @param velocityY Initial velocity of the fling (Y) measured in pixels per
     *        second
     * @param minX Minimum X value. The scroller will not scroll past this
     *        point.
     * @param maxX Maximum X value. The scroller will not scroll past this
     *        point.
     * @param minY Minimum Y value. The scroller will not scroll past this
     *        point.
     * @param maxY Maximum Y value. The scroller will not scroll past this
     *        point.
     */
    public void fling(int startX, int startY, int velocityX, int velocityY,
            int minX, int maxX, int minY, int maxY) {
        // Continue a scroll or fling in progress
        if (mFlywheel && !mFinished) {
            float oldVel = getCurrVelocity();

            float dx = (float) (mThresholdX - mStartX);
            float dy = (float) (mThresholdY - mStartY);
            float hyp = FloatMath.sqrt(dx * dx + dy * dy);

            float ndx = dx / hyp;
            float ndy = dy / hyp;

            float oldVelocityX = ndx * oldVel;
            float oldVelocityY = ndy * oldVel;
            if (Math.signum(velocityX) == Math.signum(oldVelocityX) &&
                    Math.signum(velocityY) == Math.signum(oldVelocityY)) {
                velocityX += oldVelocityX;
                velocityY += oldVelocityY;
            }
        }

        mMode = FLING_MODE;
        mFinished = false;

        float velocity = FloatMath.sqrt(velocityX * velocityX + velocityY * velocityY);

        mVelocity = velocity;
        mDuration = getSplineFlingDuration(velocity);
        mStartTime = AnimationUtils.currentAnimationTimeMillis();
        mStartX = startX;
        mStartY = startY;

        float coeffX = velocity == 0 ? 1.0f : velocityX / velocity;
        float coeffY = velocity == 0 ? 1.0f : velocityY / velocity;

        double totalDistance = getSplineFlingDistance(velocity);
        mDistance = (int) (totalDistance * Math.signum(velocity));

        mMinX = minX;
        mMaxX = maxX;
        mMinY = minY;
        mMaxY = maxY;

        mThresholdX = startX + (int) Math.round(totalDistance * coeffX);
        // Pin to mMinX <= mThresholdX <= mMaxX
        mThresholdX = Math.min(mThresholdX, mMaxX);
        mThresholdX = Math.max(mThresholdX, mMinX);

        mThresholdY = startY + (int) Math.round(totalDistance * coeffY);
        // Pin to mMinY <= mThresholdY <= mMaxY
        mThresholdY = Math.min(mThresholdY, mMaxY);
        mThresholdY = Math.max(mThresholdY, mMinY);
    }

    private double getSplineDeceleration(float velocity) {
        return Math.log(INFLEXION * Math.abs(velocity) / (mFlingFriction * mPhysicalCoeff));
    }

    private int getSplineFlingDuration(float velocity) {
        final double l = getSplineDeceleration(velocity);
        final double decelMinusOne = DECELERATION_RATE - 1.0;
        return (int) (1000.0 * Math.exp(l / decelMinusOne));
    }

    private double getSplineFlingDistance(float velocity) {
        final double l = getSplineDeceleration(velocity);
        final double decelMinusOne = DECELERATION_RATE - 1.0;
        return mFlingFriction * mPhysicalCoeff * Math.exp(DECELERATION_RATE / decelMinusOne * l);
    }

    static float viscousFluid(float x)
    {
        x *= sViscousFluidScale;
        if (x < 1.0f) {
            x -= (1.0f - (float)Math.exp(-x));
        } else {
            float start = 0.36787944117f;   // 1/e == exp(-1)
            x = 1.0f - (float)Math.exp(1.0f - x);
            x = start + x * (1.0f - start);
        }
        x *= sViscousFluidNormalize;
        return x;
    }

    /**
     * Stops the animation. Contrary to {@link #forceFinished(boolean)},
     * aborting the animating cause the scroller to move to the final x and y
     * position
     *
     * @see #forceFinished(boolean)
     */
    public void abortAnimation() {
        mCurrX = mFinalX;
        mCurrY = mFinalY;
        mFinished = true;
    }

    /**
     * Extend the scroll animation. This allows a running animation to scroll
     * further and longer, when used with {@link #setThresholdX(int)} or {@link #setThresholdY(int)}.
     *
     * @param extend Additional time to scroll in milliseconds.
     * @see #setThresholdX(int)
     * @see #setThresholdY(int)
     */
    public void extendDuration(int extend) {
        int passed = timePassed();
        mDuration = passed + extend;
        mDurationReciprocal = 1.0f / mDuration;
        mFinished = false;
    }

    /**
     * Returns the time elapsed since the beginning of the scrolling.
     *
     * @return The elapsed time in milliseconds.
     */
    public int timePassed() {
        return (int)(AnimationUtils.currentAnimationTimeMillis() - mStartTime);
    }

    /**
     * Sets the final position (X) for this scroller.
     *
     * @param newX The new X offset as an absolute distance from the origin.
     * @see #extendDuration(int)
     * @see #setThresholdY(int)
     */
    public void setThresholdX(int newX) {
        mThresholdX = newX;
        mDeltaX = mThresholdX - mStartX;
        mFinished = false;
    }

    /**
     * Sets the final position (Y) for this scroller.
     *
     * @param newY The new Y offset as an absolute distance from the origin.
     * @see #extendDuration(int)
     * @see #setThresholdX(int)
     */
    public void setThresholdY(int newY) {
        mThresholdY = newY;
        mDeltaY = mThresholdY - mStartY;
        mFinished = false;
    }

    /**
     * @hide
     */
    public boolean isScrollingInDirection(float xvel, float yvel) {
        return !mFinished && Math.signum(xvel) == Math.signum(mThresholdX - mStartX) &&
                Math.signum(yvel) == Math.signum(mThresholdY - mStartY);
    }
}

CustomViewAbove.java

  private CustomScroller mBounceScroller;
  
  void initCustomViewAbove() {
    //some code...
    mBounceScroller = new CustomScroller(context, new CustomBounceInterpolator());
  }
  
  public void scrollWithBounceInterpolator() {
  	int x = mViewBehind.getBehindWidth();
		int y = 0;
		if (getChildCount() == 0) {
			// Nothing to do.
			setScrollingCacheEnabled(false);
			return;
		}
		int sx = getScrollX();
		int sy = getScrollY();
		int dx = x - sx;
		int dy = y - sy;
		mBounceScroller.startScroll(sx, sy, dx, dy, 1000, 0, 0);
		invalidate();
	}
  
  @Override
  public void computeScroll() {
		if (!mBounceScroller.isFinished()) {
			if (mBounceScroller.computeScrollOffset()) {
				int x = mBounceScroller.getCurrX();
				int y = mBounceScroller.getCurrY();

				scrollTo(x, y);

				// Keep on drawing until the animation has finished.
				invalidate();
				return;
			}
		}
		if (!mScroller.isFinished()) {
			if (mScroller.computeScrollOffset()) {
				int oldX = getScrollX();
				int oldY = getScrollY();
				int x = mScroller.getCurrX();
				int y = mScroller.getCurrY();

				if (oldX != x || oldY != y) {
					scrollTo(x, y);
					pageScrolled(x);
				}

				// Keep on drawing until the animation has finished.
				invalidate();
				return;
			}
		}

		// Done with scroll, clean up state.
		completeScroll();
	}

SlidingMenu.java

  public void scrollWithBounceInterpolator(){
  	mViewAbove.scrollWithBounceInterpolator();
	}

Absolutely, that could be interesting. Try to play with the maths (in the interpolator) and you will find some fancy things :D

How to make it bounce only once? I could hardly understand Math used by you.