4.10 The dynamic behavior of the liquid level in cach leg of a manometer tube, responding to a change in pressure, is given by dt2d2h+R26dtdh+23Lgh=4L3p(t) where h(t) is the level of fluid measured with respect to the initial steady-state value, p(t) is the pressure change, and R, L,g,, and are constants. (a) Rearrange this equation into standard gain-time constant form and find expressions for K,, in terms of the physical constants. (b) For what values of the physical constants does the manometer response oscillate? (c) Would changing the manometer fluid so that (density) is larger make its response more oscillatory, or less? Repeat the analysis for an increase in (viscosity)