A baseball bat has a "sweet spot" where a ball can be hit with almost effortless transmission of energy. A careful analysis of baseball dynamics shows that this special spot is located at the point where an applied force would result in pure rotation of the bat about the handle grip.

Determine the location of the sweet spot of the bat shown in the figure (Figure 1) . The linear mass density of the bat is given roughly by (0.61+3.3x2)kg/m, where x is in meters measured from the end of the handle. The entire bat is 0.80 m long. The desired rotation point should be 5.0 cm from the end where the bat is held. [Hint: Where is the cm of the bat?]

find Xs.