zero

$m0$

$s$

infinite

Consider a very large mass $M(M).$ In this case, the sponge should not move, so we expect Taking the limit $M$ in the equation above indeed gives

$$

Next, consider the limit $-$ In this case, $s=0,$ which is reasonable because the spring would need to have $$ elastic potential energy to move the ball, so the ball would not move and therefore the sponge would not move.

In the limit $$ we also find $s=0,$ which is reasonable because a ball of mass would exert zero impulse on the sponge.

We can also consider $x$ and $x0,$ which should give $$ and respectively. This is confirmed by taking these limits in the equation for $s.$