A U-tube manometer is a simple device used to measure the pressure in a fluid motion. It is filled with water, and the equilibrium level of the water in the two legs is at $ y = 0 $. In the absence of friction, the level in the leg is governed by the ordinary differential equation (ODE):\[L \frac{d^2y}{dt^2} = -2gy,\]with $ L = 0.1 \, \text{m} $ being the total length of the U-tube and $ g = 9.80 \, \text{m/s}^2 $ is the gravitational acceleration constant. At $ t = 0 $: $ y(0) = 0.025 \, \text{m}, \, \dot{y}(0) = 0 $.(1) Reduce the second-order ODE to a system of two first-order ODEs.

Here, we have to reduce the second order ODE to system of first-order two ODEs. Given that…

Answered: Reduce the second-order ODE to a system…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Reduce the second-order ODE to a system of two first-order ODEs;