It would be trivial to calculate the motion of a pendulum if displacement is assumed small and if an infinitely rigid rod is assumed to connect the boundary and the mass.

Satisfying the first assumption is easy. All we have to do is maximize the mass ratio. However, we cannot easily satisfy the second assumption. In fact, it would probably be better if we used something similar to a frictionless string.

#1 Aesthetics aside, what would you consider to be the ideal material that approaches the behavior of a "frictionless" string?

#2 I assume the string will have resonances (I think this is why StigErik chose to use rubber for his material). How would you calculate this? The boundary condition does not equal zero. Would that make it an inhomogeneous differential equation?

#3 How would the equations change if a 3D swing (ie you might visualize it as a tripod that is inverted and whose rods are replaced by strings) compared to a swing with a single string?

#4 What would you consider to be the minimum mass ratio? It would appear that the displacement of the pendulum would have a negligible effect on the response of the loudspeaker, UNLESS its displacement approached the dimensions of the highest reproduced wavelength. Would you consider 1/(highest reproduced wavelength*10) to be a good rule of thumb for maximum allowable displacement of the pendulum?

Thanks,

Thadman

Satisfying the first assumption is easy. All we have to do is maximize the mass ratio. However, we cannot easily satisfy the second assumption. In fact, it would probably be better if we used something similar to a frictionless string.

#1 Aesthetics aside, what would you consider to be the ideal material that approaches the behavior of a "frictionless" string?

#2 I assume the string will have resonances (I think this is why StigErik chose to use rubber for his material). How would you calculate this? The boundary condition does not equal zero. Would that make it an inhomogeneous differential equation?

#3 How would the equations change if a 3D swing (ie you might visualize it as a tripod that is inverted and whose rods are replaced by strings) compared to a swing with a single string?

#4 What would you consider to be the minimum mass ratio? It would appear that the displacement of the pendulum would have a negligible effect on the response of the loudspeaker, UNLESS its displacement approached the dimensions of the highest reproduced wavelength. Would you consider 1/(highest reproduced wavelength*10) to be a good rule of thumb for maximum allowable displacement of the pendulum?

Thanks,

Thadman

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