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

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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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.
Transcribed Image Text: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.
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