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Yes, you are right. If it helps try to imagine a horizontal spring with two equal masses at the two ends on a frictionless surface, vibrating about the center of mass of the system, which is at the middle of the length of the spring. They always have opposite and equal magnitude acceleration and velocity and displacement.

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Regarding your first question IMHO eigenvalue analysis is appropriate and valid as long as the material is within the elastic range. Also another misconception is that, the application of eigenvalue analysis depend on how close the excitation frequency to the fundamental frequency. (In actuality, IMHO you can regard the cymbals case as an impulse, not as a ...

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Strain is the ratio of change in length of a layer of fiber in the beam with respect to its original length. And it is a function of displacement (elongation/shortening) in direction of the longitudinal axis, x, at time t (for the changes, length and sign, are dynamic in nature).

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First of all, before looking at any solution, you need to characterize two things the frequency of the vibrational input, which you can measure by placing an accelerometer on the floor. There is a quite good 3axis accelerometer built into every smart phone, so download the appropriate app (there are free ones that are more than good enough), take ...

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As you know you already had better results with softer compounds. So if you image the solid block as a spring, then you need a spring with a lower coefficient K. So you need to have higher displacement for a given force to follow hooke's law: $$F = - K\cdot x$$ Now, the solid block isn't immediately recognizable as a spring, however you can estimate it as a ...

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First of all, there will be two deflection equations, because the stiffness is not uniform. I'm getting the impression you somehow tried to use a single equation for the whole beam, which would obviously fail. The basic equation for cantilever beam you posted seems correct. Now for the left part you can use that as is, substituting the total length (L1+L2) ...

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