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Another solution to the wave equation presented by Chopra. Chopra (1967) presented a closed form solution for hydrodynamic pressure in the case of rigid dam with the vertical up-stream face under the horizontal and vertical ground motion. For the excitation frequency less than the fundamental frequency of the reservoir, both Westergaard and Chopra's solution are the same. The greater excitation frequency causes an out-of-phase pressure compared to Westergard's solution. In this case the hydrodynamic pressures cannot be represented by inertia effect on an added mass moving with the dam. Also it was found that the response to vertical ground motion is a real valued function and there is no decay with time so that the system is truly undamped in this case.

In his solution for the horizontal earthquake, the wave equation for a rigid dam with rectangular reservoir (figure 2.18)presented subjected to the following boundary conditions:

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