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Natural Science Forum / Physics / Acoustics / December 2005Vibration of baseball bat
am just a physics student. When a free-on-both-ends object like a baseball bat(is it considered free if you are holding at one end?) is impulsively struck it vibrates at its natural frequnecy. But doesn't it also vibrate at higher modes? What determines how it gets to those modes? I know frequency determines the mode, but what about between modes, does it just vibrate at the lower mode and then when just enough more impulsive energy, like from a harder baseball hit, does it jump up like a phase jump to the next frequency. Or, in between modes, when you are moving the frequency up, presumably with a harder hit, does the wave "flat-line" and then only resonate at just the right frequency for the next particular modes? Can a harder hit on a free object stimulate higher modes; or does it just stay and only vibrate at the lowest natural frequency and a higher amplitude is the only result of higher imulsive energy input? IE: when a free object is struck can it vibrate at other frequencies other than the natural frequency and what happens if it does? Thank you so much in advance, I have searched hard and long everywhere for this answer. PS If holding at one end causes a node there does the bat then vibrate like a closed pipe(only odd harmonic modes) you see described in physics textbooks? Pierce, > When a free-on-both-ends object like a baseball bat < I can't answer your questions, but maybe this will help: http://www.kettering.edu/~drussell/bats.html --Ethan > http://www.kettering.edu/~drussell/bats.html Took the words right out of my mouth... Chris W  SignatureThe voice of ignorance speaks loud and long, But the words of the wise are quiet and few. --- Browsing here might help you visualise what is going on: http://www.falstad.com/mathphysics.html several of the examples allow you to strike a structure and look at the modes. > Browsing here might help you visualise what is going on: > http://www.falstad.com/mathphysics.html > several of the examples allow you to strike a structure and look at the > modes. The baseball bat is not there. The simplest would be a bar of two diameters, heavy right and light left, for instance. Angelo Campanella > am just a physics student. Hopefully not yet third or fourth year college level. > When a free-on-both-ends object like a baseball bat >(is it considered free if you are holding at one end?) Yes. > is impulsively struck it vibrates at its natural frequnecy. But doesn't > it also vibrate at higher modes? Yes > What determines how it gets to those > modes? The boundary conditions. I know frequency determines the mode, Not exactly, but there is a resonant frequency and mode shape associated with each mode. > but what about between > modes, does it just vibrate at the lower mode and then when just enough [quoted text clipped - 3 lines] > wave "flat-line" and then only resonate at just the right frequency for > the next particular modes? The frequency response funciton specifies the vibration amplitude. If the excitation is sinusoidal, the maximum vibration amplitude will occur at the resonant frequencies. Between the resonant frequencies the vibration amplitude will be lower. If the excitation impulsive, several modes will be excited. Which modes are excited will depend on the point of excitation, the spectral content of the excitation and the boundary conditions. The vibration associated with each of the excited modes will decay in accordance with the loss (damping). > Can a harder hit on a free object stimulate > higher modes; or does it just stay and only vibrate at the lowest > natural frequency and a higher amplitude is the only result of higher > imulsive energy input? If the system is linear, the number of modes that are excited will not depend on the amplitude of the excitation. > IE: when a free object is struck can it vibrate > at other frequencies other than the natural frequency and what happens > if it does? Vibration and resonance are not synonymous. When a free object is struck impulsively its motion will contain energy over a wide range of frequencies. However, between between resonant frequencies the vibration amplitude will be low and the contritubtion to the total vibration will not be oscillatory. > Thank you so much in advance, I have searched hard and long everywhere > for this answer. Interesting, because a 5-second google search for baseball bat vibration comes up with the following link at the top of the list. http://www.kettering.edu/~drussell/Demos/batvibes.html > PS If holding at one end causes a node there does the bat then vibrate > like a closed pipe(only odd harmonic modes) you see described in > physics textbooks? Holding one end does not cause a node there. The bat vibrates essentially with low impedance at both ends, which is the mechanical equivalent of an open organ pipe. > am just a physics student. When a free-on-both-ends object like a > baseball bat(is it considered free if you are holding at one end?) My recollection of the baseball bat problem is that one wants the ball to strike at the center of percussion of the bat. This is near the center of gravity, but there is the matter of the bat rotating as it strikes, so I'll leave that to the up-to-date experts here. > is > impulsively struck it vibrates at its natural frequnecy. The first mode I can think of the the "xylophone mode", where, for a straight stick, it has nodes (no-motion points) about 25% in from each end. The center of percussion is defined as that point on a stick or body where, when struck (*not* for mumbly pegs), the result is pure translation with no rotation. A uniform stick would have that point at its center. Baseball bats are tapered, with most mass on the outer half, making the center of gravity and the center of percussion, out at about 25%-30% from the end, and being near the xylophone null node. > But doesn't > it also vibrate at higher modes? The higher modes in this case are higher xylophone modes. These are modes where there is no net moment on the stick (no node at the center). > What determines how it gets to those > modes? I know frequency determines the mode, but what about between [quoted text clipped - 4 lines] > wave "flat-line" and then only resonate at just the right frequency for > the next particular modes? Can a harder hit on a free object stimulate With an impulse (duration of contact with ball is much shorter than a single cycle of a mode), all modes can be excited depending on the contact point as related to the loops (they accept energy) and nodes (they do not accept energy) of each individual mode. They "ring" for a length of time depending on their damping (and are felt by the batter's hands). > higher modes; All modes that can be excited by an impulse at the contact point are excited, their duration being determined by the damping offered by the batter's hands. > or does it just stay and only vibrate at the lowest > natural frequency and a higher amplitude is the only result of higher > imulsive energy input? IE: when a free object is struck can it vibrate > at other frequencies other than the natural frequency and what happens > if it does? There can be vibration at other frequencies, but only the natural modes (eigenmodes; all that we have discussed) will absorb a significant amount of energy and vibrate for some time afterwards. > PS If holding at one end causes a node there does the bat then vibrate > like a closed pipe(only odd harmonic modes) you see described in > physics textbooks? Holding the bat at one end is not the whole story. It is mighty preferable that the batter have the ball strike the center of percussion of the bat and nowhere else, since that is where the greatest energy transfer to the ball will result (greatest range for the ball), since little or no energy is absorbed by the bat. Energy is shared or absorbed by; accelerating the ball to go on its way as desired, by exciting vibration eigenmodes in the bat, and by stinging the batter's hands (ouch!) when the impact is not on the center of percussion. Since the bat is already rotating when it impacts the ball, one wants that rotational rate to be unchanged (no sting, please) by the impact; no rotational rate change on account of the impact (i.e. impact at the center of percussion). Angelo Campanella |
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