(Solved): 18 Example 15 The location center of percussion P for a rigid body is given by: \( h=I_{O} / m d \), ...

18 Example 15 The location center of percussion P for a rigid body is given by: \( h=I_{O} / m d \), where \( h \) is the distance from the support point O to \( \mathrm{P}, d \) is the distance from the support point O to the center of mass G and \( I_{O} \) is the mass moment of inertia of the body about the support point O . In this example, we will explore using the free vibration response of a baseball bat suspended from support point O to determine the location of the bat's center of percussion. 1. Draw an FBD of the bat. 2. Develop the equation of motion (EOM) of the bat in terms of the angle \( \theta \). Linearize this EOM for small \( \theta \) (recall that for small \( \theta \) we have \( \sin \theta \approx \theta \) ). 3. Based on your linearized EOM, what is the natural frequency of free response of the bat in terms of the parameters of the problem? 4. Determine the relationship between the distance \( h \) to the center of percussion and the natural frequency of free oscillations for the bat. 5. Discuss how you could set up a simple experiment to determine the location of the center of percussion of the bat.